
	Where results make sense

Topic: Separable differential equation

In the News (Tue 22 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Making a differential equation separable (Site not responding. Last check: 2007-10-11)
		In the last example in the previous section, we had to rearrange the right-hand side of the differential equation before we could separate the variables.
		The equation is then written entirely in terms of this new variable and x.
		To write the differential equation in terms of x and v(x), instead of x and y(x), we replace all occurrences of y by vx.
	www.ucl.ac.uk /Mathematics/geomath/level2/deqn/de7.html (326 words)

	Differential Equations (Math 3401) - First Order DE's - Separable Equations
		Note that in order for a differential equation to be separable all the y's in the differential equation must be multiplied by the derivative and all the x's in the differential equation must be on the other side of the equal sign.
		This differential equation is clearly separable, so let's put it in the proper form and then integrate both sides.
		This differential equation is easy enough to separate, so let's do that and then integrate both sides.
	tutorial.math.lamar.edu /AllBrowsers/3401/Separable.asp (1738 words)

	Separable differentiable equations and chemical kinetics
		Separable differential equations can often be solved analytically by a technique known as separation of variables.
		For separable differential equations, it should be clear that the solution process always introduces a constant of integration.
		Separable differential equations often appear in chemical kinetics, which is the study of rates of chemical reactions.
	www.math.wpi.edu /Course_Materials/Calc3/Labs/node2.html (785 words)

	First Order Differential Equations
		In any situations where this is possible, the solution of the differential equation reduces to that of evaluating the integrals on each side of the separated equation.
		Thus we will assume that the differential equations with which we must deal from now on are not separable in the sense described here.
		Since we have eliminated consideration of the separable differential equation, we can conclude that f(x,y) cannot be written as the product of a function of y only and a function of x only, for otherwise, we could separate the y and x parts of the equation.
	pathfinder.scar.utoronto.ca /~dyer/csca57/book_P/node46.html (427 words)

	Assignment for
		I was concerned that a unit on differential equations would be difficult to teach without differentiating because I knew that I had not emphasized these problems last year, but that the other teacher had.
		I hypothesized that my students would likely fall into three categories that I had labeled as (1) those who had a complete grasp of separable differential equations and their applications, (2) those who were moderately comfortable and (3) those who were clueless.
		Since this was a topic that was covered to some extent by all students, and it was the foundation for further lessons on slope fields and Euler’s method, I felt that the students would benefit from learning, reviewing, or extending their knowledge of the real-world applications of differential equations before taking on the new material.
	www.rvgs.k12.va.us /differentiation_files/equation.htm (908 words)

	2
		singular solution to a differential equation is a solution that is not found as a member of a general solution for the differential equation.)
		The above differential equation is used to model populations over short periods of time.
		This is a separable (and a linear) differential equation.
	www.gpc.edu /~jcraig/de_notes/1s4.htm (529 words)

	sepde
		The solutions of differential equations involve finding the inverse of some problem stated with derivatives.
		In this section, we examine a class of differential equations that can be separated into two integration problems to form the solution of the differential equation.
		We noted earlier that differential equations are difficult in general to solve.
	www-rohan.sdsu.edu /~jmahaffy/courses/f00/math122/lectures/sep_diffequations/sepdiffeq.html (974 words)

	Differential Equations Lecture Notes, 09/11/03 (Site not responding. Last check: 2007-10-11)
		In this chapter we will examine "first-order" differential equations, which are simply differential equations of the form F(x,y,y') = 0 that do not contain any derivatives of y higher than the first derivative.
		Definition: A first-order differential equation is said to be separable if it has the form dy/dx = g(x)/f(y) for some functions g and f.
		To solve a separable differential equation we rewrite it in the form f(y)*dy/dx = g(x), then integrate each side with respect x.
	www.assumption.edu /Alfano/MAT355-FA03/Notes/091103.html (414 words)

	An Introduction to Differential Equations
		A differential equation is an equation that defines a relationship between a function and one or more derivatives of that function.
		In differential equations the unknowns of concern are no longer unknown variables, but unknown functions that stand in certain mathematical relationships with their derivatives, other functions, constants, and regular variables.
		And to continue the analogy yet some more, just as the equations with which you are familiar are classified into types according to their forms and solution techniques, so to with differential equations.
	www.physics.ohio-state.edu /~physedu/mapletutorial/tutorials/diff_eqs/intro.html (586 words)

	Introduction to Differential Equations, part 5
		For such an equation, obtaining a general description of the solutions is the same as finding all antiderivatives of f, i.e., the same as calculating an indefinite integral.
		Below is a slope field for this differential equation with this particular solution displayed.
		Note that this is our rumor-spreading differential equation from Part 1 with k and M both set equal to 2.
	www.math.duke.edu /education/ccp/materials/postcalc/ode/ode5.html (876 words)

	[No title]
		This is such a well known equation that unless they specifically tell you to solve it while showing your steps, you can just skip straight to the solution, given in box 2 on p604.
		Section 9.5 -- Logistic Equation ----------- We didn't spend as much time on this as on other differential equations, and usually that means it won't be as important on the test.
		Areas with parametric equations weren't stressed at all in class, and you only had a few homework problems on this, so it's probably not as important.
	www.math.umn.edu /~rogness/calc1372/midterm2.txt (1826 words)

	Differential Equations (Math 3401) - First Order DE's - Exact Equations (Site not responding. Last check: 2007-10-11)
		Likewise if (5) is not true there is no way for the differential equation to be exact.
		So, the differential equation is exact according to the test. However, we already knew that as we have given you Ψ(x,y). It’s not a bad thing to verify it however and to run through the test at least once however.
		Now, as we saw in the separable differential equation section, this is quadratic in y and so we can solve for y(x) by using the quadratic formula.
	tutorial.math.lamar.edu /AllBrowsers/3401/Exact.asp (1834 words)

	7 (Site not responding. Last check: 2007-10-11)
		separable differentiable equation is a differential equation in which the expression for
		To solve a separable differential equation, integrate both sides of
		singular solution (a solution which is not obtained from the general solution for the differential equation).
	www.gpc.edu /~jcraig/calc2_ch7/7s3_separable_equations.htm (316 words)

	Untitled Document (Site not responding. Last check: 2007-10-11)
		Last time we solved a differential equation by the method of separation of variables.
		This is one of my favorite differential equations books, it starts out at an elementary level and includes nonlinear equations and partial differential equations.
		Vladimir I. Arnold (1973), Ordinary Differential Equations, MIT Press (as of 1991 in its 8th printing, translated from the Russian by Richard A. Silverman).
	www.sas.org /E-Bulletin/2004-02-06/mathCorner/body.html (464 words)

	Front Page for Module 8: Differential equations (Site not responding. Last check: 2007-10-11)
		In the real world, an enormous number of physical processes can be modelled by differential equations - processes such as air flow around an aircraft wing and heat flow in the earth's core or atmosphere.
		You may recall that in the introduction to module 6, we said that an integral of a function which is exactly the derivative of another function was called a closed form integral.
		In the same way, many differential equations are not closed form, and cannot be solved directly.
	www.es.ucl.ac.uk /undergrad/geomaths/8-deq/deqtoc.htm (331 words)

	diffeq (Site not responding. Last check: 2007-10-11)
		Vectorfields: This animation uses the vector field given by a separable differential equation as the background.
		The functions f and g represent the two parts of the separable differential equation dy/dx = f(x) g(y).
		The red curves are defined implicitly by the equation f(x,y) = k.
	www.plu.edu /~heathdj/mov/diffeq.html (329 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		Be able to express the total center of mass (centroid) as a limit of the center of mass of a differential element.
		Be able to solve a separable differential equation - know how to get the general and/or the particular solution.
		Be able to sketch the graph of a parametric curve and indicate the direction in which the curve is traced as the parameter increases.
	www.math.colostate.edu /~peters/M160_161/review2.htm (367 words)

	Intro (Site not responding. Last check: 2007-10-11)
		This document provides a listing of several types of ordinary differential equations that we will encounter throughout the first three weeks of our study of differential equations.
		A differential equation is called separable, if we are able to separate the variables using only elementary algebraic manipulations.
		One common form of writing a separable differential equation would be as follows.
	www.nav.cc.tx.us /staff_pages/math/robrien/Intro.html (159 words)

	Separable Differential Equations
		In case you've forgotten, we'll remind what a differential equation is and why they are so useful in mathematics.
		Here we are given a differential equation and an initial value (we usually call these two pieces of information an initial value problem).
		Sometimes we are presented with a family of curves in the plane and we would like to know the trajectory of a point which is always moving orthogonally to the curves.
	www.ugrad.math.ubc.ca /coursedoc/math101/notes/moreApps/separable.html (1418 words)

	Nonlinear Second Order Differential Equations
		This is a first order linear differential equation.
		This is again a first order differential equation.
		Since this is a separable first order differential equation, we get, after resolution,
	www.sosmath.com /diffeq/second/nonlineareq/nonlineareq.html (157 words)

	Study Guide 1 (Site not responding. Last check: 2007-10-11)
		Given a population P whose growth is governed by the differential equation P' = k P, how does the sign of k relate to the long-term survival of the population?
		A spring-mass system is governed by a second order differential equation mx'' + cx' + kx =F(t), where m represents the mass, x(t) represents the displacement of the mass at time t, c is the damping constant, k is the spring constant, and F(t) is the external force.
		Answer: The term kx represents the restoring force exerted by the spring, which is proportional to the displacement of the spring.
	www-math.cudenver.edu /~billups/courses/ma3200/study1.html (202 words)

	MATH 20
		Find the general solution of the separable differential equation y’ = 9x
		Find the solution to the differential equation and find the constants.
		Solve the first-order linear differential equation(x + 1)y’ + y = 2x.
	www.emba.uvm.edu /~puterbau/math20fall2002/quiz8answers.htm (63 words)

	[No title]
		The solution to the differential equation is the sum of the particular solution just found the homogenous solution from equation [ SEQ eqn e94 94].
		The equation and the initial conditions are entered as string arguments to this function.
		The differential equation d2y/dx2 + 3 dy/dx + 2y = ex cos x is specified in MTALAB as the following formula: ‘D2y + 3 * Dy + 2 * y = exp(x) * cos(x)’.
	www.csun.edu /~lcaretto/me501a/ODE.doc (967 words)

	ap7.html
		On the axes provided, sketch a slope field for the differential equation at the eleven indicated points.
		The differential equation in the AP problem and the one in the example above are both called
		Use Maple to make a slope field for the differential equation of the AP problem.
	www.uwec.edu /smithaj/Summer710/ap7.html (192 words)

	7.8 Differential Equations - Variables Separable
		an application of the indefinite integral, the one to differential equations.
		In the remainder of this section the abbreviation “DE” stands for “differential equation”.
		A variables-separable (or separable) differential equation is one of the form:
	www.geocities.com /pkving4math2tor7/7_app_of_the_intgrl/7_08_diffl_eq_var_sep.htm (811 words)

	Lab5-help
		You will be solving the differential equations using the Excel worksheet with numerical methods for differential equations that is provided via a hyperlink.
		You will compare your numerical solution to the actual solution, which in both cases is a separable differential equation.
		At the end of this problem, your graph should show you the differences between the two solutions and show how well the easier equation approximates the time of death.
	www-rohan.sdsu.edu /~jmahaffy/courses/s04/math122/labs/lab5/lab5-help.html (398 words)

	No Title (Site not responding. Last check: 2007-10-11)
		By solving the separable differential equation, find the exact value of y(1).
		By solving the separable differential equation, determine when the solution will be distance 1 away from the stable equilibrium, if y(0)=3.
		, which may be found by solving the separable differential equation, or just knowing that solutions must decay exponentially toward R with decay constant k.
	www.math.sunysb.edu /~detlef/127s00/mat127finsampsol/mat127finsampsol.html (793 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		Explain why this technique for solving a separable differential equation works.
		Give an example of a differential equation which can be solved by means of an integrating factor.
		Give several examples of applications of differential equations -- radioactive decay, population growth, mixture problems.
	bradley.bradley.edu /~delgado/122/Review2.f01.txt (367 words)

	Mth 336 Differential Equations Calendar (Site not responding. Last check: 2007-10-11)
		Section 1.1: Understand basic concepts of what a differential equation is and the terminology used for different forms of differential equations.
		From Section 1.2: Understand what is meant by a solution to a differential equation or an intial value problem.
		Be able to determine whether a differential form is exact and when a differential equation is exact.
	www.saintjoe.edu /~karend/m336/m336a.html (894 words)

	Separable Differential Equations
		on the left hand side of the equation and all of the
		Substitute to rewrite the differential equation in terms of
		Follow the steps for solving separable differential equations.
	www.ltcconline.net /greenl/courses/106/approxother/SEPDIF.HTM (154 words)

	Separable Differential Equations
		This is a tutorial on solving separable differential equations of the form
		Depending on f(x) and g(y), these equations may be solved analytically.
		We first rewrite the given equations in differential form and with variables separated, the y's on one side and the x's on the other side as follows.
	www.analyzemath.com /calculus/Differential_Equations/separable.html (248 words)

Try your search on: Qwika (all wikis)