Integrating factor Definition and 113 Threads

Homework Statement My book shows that http://img845.imageshack.us/img845/4875/unleduot.jpg and then they arrived at the results [PLAIN][PLAIN]http://img202.imageshack.us/img202/5442/unleddq.jpg So my problem is that, how exactly did they drop the mu in the first picture?

Homework Statement "Show that each of the given differential equations of the form M(x,y)dx + N(x,y)dy = 0 are exact, and then find their general solution using integrating factors μ(x) = e∫h(x)dx and μ(x) = e∫g(y)dy Homework Equations (x2 + y2 + x)dx + (xy)dy = 0The Attempt at a Solution...

Homework Statement (2x+y^2) dx +4xy dy=0,y(1)=1 Homework Equations The Attempt at a Solution I'm having trouble finding the correct integrating factor, been playing with it for an hour and have made NO progress so need help. \delta P/\delta y=2y \delta Q/\delta x=4y...

I was looking at how to derive an integrating factor for a non-exact DE that has multiple variable dependency, i.e. µ is xy-dependent, and I found the explanation at the link in the middle of the page at equation (22) (link...

Homework Statement Integrate dy/dx=2y+4x+10 The Attempt at a Solution dy/dx-2y=4x+10 Integrating factor = e^(-2)dx=e^-2x multiply both sides by IF. (e^-2x)dy/dx-2y(e^-2x)=(e^-2x)(4x+10) dy/dx(e^-2x y)=(e^-2x)(4x+10) i don't know what to do next.

Homework Statement Sorry asking similar quesion again about absolute value. You can read the attachment. u(x) is the integrating factor. Why absolute value is omitted in the integration? and why the integrating factor is not "1/|x|", with the absolute sign Homework Equations The...

Homework Statement Multiply the given equation by the given integrating factor and solve the exact equation. Homework Equations ydx+(2x-yey)dy=0, \mu(x,y)=y. The Attempt at a Solution M=y2, N=2xy-y2ey Integrating N=\Psiy WRT x I get xy2-((1/3)y3ey + y2ey)+h(x)=\Psi(x,y) Differentiating...

Homework Statement use an integrating factor to solve \frac{ \partial u}{ \partial x} = -2 + \frac{u}{2x} The Attempt at a Solution let P(x) = \frac {1}{2x} M(x) = e^(\int(\frac {1}{2x}dx)) = \sqrt{x} so u = \frac{1}{ \sqrt{x}}...

Hello All, Given the equation (2/y + y/x)dx + (3y/x + 2)dy I am first asked to show the equation is not exact. To do this I showed the mixed partials were not equal i.e.: (2/y + y/x)dy != (3y/x + 2)dx I am then asked to find an integrating factor and show the potential function is given...

Homework Statement xy' - 4y = x4ex Homework Equations The Attempt at a Solution y' - 4x-1y = x3ex x-4y' - 4x-5y = x-1ex I'm not sure what to do next, I can't express the LS as a derivative

greetings what does a integrating factor tells about a differential equation? in order to find the solution for a exact equation we multiply the equation by integrating factor(I.F). as intergrating factor=e^integration(p)dx i.e given by I.F=e^gx where gx is integration of p now as we have...

Hello I'm trying to solve the following DGL with an integrating factor: x'=xg(y) y'=yh(x) which is equivalent to -yh(x)dx+xg(x)dy=0 which is an inexact dg? How to i find an integrating factor in this case? thx

Homework Statement Solve the differential equation with the initial condition y(0) = 1 Homework Equations 3e5xdy/dx = -25x/y2 The Attempt at a Solution First I tried putting everything with an x or dx on one side and a y or dy on the other side, and solved for C. I got 0 as the...

Hello all! :smile: I through a section in my text (by https://www.amazon.com/dp/0133214311/?tag=pfamazon01-20) on 1st Order linear ODEs. I am understanding the derivation of the integrating factor method pretty well; however, there are some aspects of the mathematics that I am getting hung up...

First order nonlinear ODE -- Integrating factor + exact differentials, or not? Hello everyone, (I apologize if this did not format properly, if not I will attempt to edit it if that functionality is available upon submitting a question). I recently came across the following nonlinear ODE...

Homework Statement Solve the inital value problem for y(x); xy′ + 7y = 2x^3 with the initial condition: y(1) = 18. y(x) = ? Homework Equations dy/dx +P(x)y=Q(x), integrating factor=e^∫P(x) dx The Attempt at a Solution Multiplied all terms by 1/x to get it in correct form...

Homework Statement Solve (x + 2) sin y dx + x cos y dy = 0 by finding an integrating factor .....M......N..... M_y (x+2)siny = (x+2)cosy N_x xcosy = cos y M_y not equal to N_x, therefore equation is not exact.. so far so good? thanks Homework Equations The Attempt at...

Verifying an integrating factor --please check my work , thanks. Homework Statement Verify that 1/y^4 is an integrating factor for (3x^2-y^2)dy/dx - 2xy = 0, and then use it to solve the equation (1/y^4)* (3x^2-y^2)dy/dx = 2xy* (1/y^4) =3x^2 / y^4 dy = 2x/y^3 dx =3x^2 / y dy = 2x...

Homework Statement my integrating factor for the DE ty' + (t+1)y = t is mu(x) = e^integ (1+(1/t)) = e^(t + ln|t| + c) so does this simplify to this...or not? = e^t + t + c so that DE becomes: ((e^t) + t))y = (e^t) + t) and then after integrating... ((e^t) + t))y = e^t +...

Homework Statement Solve: (1-\frac{x}{y})dx + (2xy + \frac{x}{y} + \frac{x^2}{y^2})dy = 0 The Attempt at a Solution No idea what strategy to use here. Tried using an integrating factor, but no success. A lot of x/y in here makes me think I need to use a substitution, but there's also...

Homework Statement solve the following initial condition problem x (d/dx) y(x) + 4xy(x) = -8-y(x) y(4)=-6 Homework Equations The Attempt at a Solution first i rearranged xy'+y+4xy=-8 xy'+y(1+4x)=-8 y'+y(1/x+4)=-8/x integrating factor:e^\int(1/x+4) e^(lnx+4x) x+e^4x multiplying...

y' + y = e^x ; y(0) = 1 1st, i calculate the integrating factor... u(x) = e^x times the integrating factor with DE... y'e^x + ye^x = e^2x dy/dx e^x + ye^x = e^2x d/dx ye^x = e^2x ye^x = ∫ e^2x dx ...= 1/2 e^2x + C y = 1/2 e^x + C the problem here, i didn't get the...

Question: (1 - x - z)dx + dz = 0 let M = (1 - x - z) ; N = 1 dM/dz = -x ; dN/dx = 0 hence, not exact. integrating factor... 1/N[ dM/dz - dN/dx ] = 1[-x] .......= -x e^∫-x dx = e ^ [(-x^2)/2] times integrating factor with DE.. {e ^ [(-x^2)/2] -x e ^ [(-x^2)/2] - z e ^...

y dx + x ln x dy = 0 ; x > 0 my integrating factor is x.. so.. multiply with DE, xy dx + x^2 ln x dy = 0 let M = xy ; N = x^2 ln x dM/dy = x ; dN/dx = x + 2x ln x the problem is.. i didn't get the exact equation after multiply the integrating factor.. I've double...

Homework Statement Show that given function μ is an integrating factor and solve the differential equation.. y^2 dx + (1 + xy) dy = 0 ; μ(x) = e^xy The Attempt at a Solution let M = y^2 N = (1 + xy) dM/dy = 2y dN/dx = y hence, not exact equation. times μ(x) = e^xy to the...

([SIZE="2"]Moderator's note: thread moved from "Differential Equations") M(x,y) + N(x,y)(dy/dx) = 0 f'(xy) = G(xy)f(xy) where G(xy) = (Nx - My)/(xM - yN) Replace xy with a single variable to obtain a simple 1st order differential equation and find f(xy). I got to: ln|f| =...

Integrating factor! As promised I'm back with integrating factor differential equation.(x^2 + 1)dy/dx -2xy = 2x(x^2+1) y(0)=1 First put into standard from by dividing thru by (x^2 +1 )dy/dx -2xy/(x^2 + 1) = 2x Integrating factor is given by exp( integral of -2x(x^2 + 1))...

Homework Statement Find all solutions of the equation: y' = (2y)/(t.logt) = 1/t, t > 0 Homework Equations Integrating factor I = exp(\intp(x)dx) where y' + p(x)y = q(x) The Attempt at a Solution Hi everyone, here's what I've done so far: Let p(t) = -2/(t.logt) I =...

whenever i see that integrating factor for solving a linear differential equation with eint. p(x) dx and then multiplied out in the equation, there seems to be no constant. i tried solving an equation with it the other day, and got an incorrect solution because of it (i think. at least i got a...

Hi, I tried to solve this by using the integrating factor technique \begin{cases} dy/dt +10y = 1 \\ y(1/10) = 2/10 \end{cases} So p(x) = 10t \rightarrow e^{10t} e^{10t} \cdot \frac{dy}{dt} + e^{10t} \cdot 10y = e^{10t} This part is confusing to me, i have two different variables...

Homework Statement Find general solution of equation (t^3)y' + (4t^2)y = e^-t with initial conditions: y(-1) = 0 and t<0 book answer gives y = -(1+t)(e^-t)/t^4 t not = 0 Homework Equations The Attempt at a Solution (t^3)y' + (4t^2)y = e^-t get integrating...

So there's this equation: x^2 y^2 dx + (x^3y-1)dy It has to be solved with the integrating factor method, so I get this: \mu(y) = e^{\int \frac{dy}{y}} = e^{\ln{|y|}} = |y| My question is, what do I do with the absolute value bars? If I just drop them and multiply the entire equation with...

Finding the integrating factor (ODEs) [Solved] Working on this problem, I can't figure out why we take the derivative of \mu with respect to y, and what to do when our integrating factor is a function of both x and y. In the case below, it ended up being separable, but what can you do if it's...

Homework Statement Solving this differential equation ty' + 2y = t^2 - t + 1 Homework Equations Its linear so i set it up in linear form y' + y(2/t) = t - 1 +1/t The Attempt at a Solution the integrating factor (u) = e ^ integral (ydt) = e^ integral (2dt/t)... Here's the...

Homework Statement The ODE is (1+x)*dy/dx - xy = x+x^2 Homework Equations The method of solution is to be through the use of the integration factor. The Attempt at a Solution First, I divided each side by (1+x) to produce dy/dx - xy/(1+x) = x then factor out the x on...

During one lecture it was mentioned that equations of the form P(x,y)dx+Q(x,y)dy=0 always have at least one integrating factor. But the lecturer didn't know the proof, I've tried using Google but no luck. Anybody can show me the proof? Thanks a lot.

what next ? TNX !

I can see why y2 is an integrating factor, but I don't know how this answer can be derived. Do you use: \frac{N_{x}(x,y) - M_{y}(x,y)}{M(x,y)} Where M (x,y) = 4(x3/y2)+(3/y)]dx, and N = 3(x/y2)+4y dy When I try and solve this, I get a very complex integrating factor...

In the following problem how does -g end up becoming -g(m/g)? Isn't the derivative of -g just (-g^2/2)? http://users.on.net/~rohanlal/integfact.jpg

I'm trying to follow this example from class notes. x^2 \frac{{dy}}{{dx}} + xy = 1,\,\,y\left( 1 \right) = 2 Divide through by x^2 to set it up in a form for using the integrating factor method. \frac{{dy}}{{dx}} + \frac{y}{x} = - \frac{1}{{x^2 }} I'm not sure where the minus...

I was given the following ODE to solve and it seemed simple enough. However, after you have used the integrating factor the integral is not integratable. y' = (1+x^2)y +x^3, y(0)=0 Find y(1) if y(x) is the solution to the above ODE. So I put it in the proper form of: y' + (-1-x^2)y...

Homework Statement Find the gerneral solution of the differential equation below: dy/dt=(-y/t)+2 Homework Equations none The Attempt at a Solution my solution by using integrating factor: 1.find the homogenous solution first dy/y = -1/t dt you get ln(y) = -ln(t) when...

Hi ok so te question is asking for me to fin the integrating factor of (y2x+y)dy + (x2y+2x)dy = 0 the only thing i know is that the integrating factor should be a function of xy Can some one pleas explain how to do this? Thank you.

Homework Statement Am I doing this correctly? Is 2y^4dx +4xy^3dy exact or inexact? Homework Equations The Attempt at a Solution So if its exact, then M(x,y)dx = N(x,y)dy right? (Euler) But how can I take partial derivative of 2y^4 with respect to x, if there is no x to...

Hello, I was looking at the differential equation (x^2 + 1) \frac{dy}{dx} + xy = 0. This solution to this equation has to be y = \frac{c}{\sqrt{x^2 +1}} So, when do we usually need to use the method of integrating factor? Can we solve all linear equations (1st order) using this method...

Easier way of finding Integrating Factor for Exact Differential Equation?? Homework Statement ,find an integrating factor and then solve the following: [4(x3/y2)+(3/y)]dx + [3(x/y2)+4y]dy = 0 Homework Equations u(y)=y2 is a valid integrating factor that yields a solution...

[SOLVED] Integrating Factor Diff Eqs Homework Statement g ' - g/t = t e^t I'm trying to solve this, but I seem to have run into a problem, according to my book the integrating factor is 1/t, however I believe that it is -t Homework Equations The Attempt at a Solution...

Hi, I'm learning differential equations, and although I understand the methods I have learned thus far, I often have trouble seeing what is the reasoning behind them. Take for example, the use of the integrating factor when solving first order linear ODE's. I understand how to use it, but...

1. Solve the equation [sin(xy) + xycos(xy)]dx + [1 +x^{2}cos(xy)dy = 0 Homework Equations The Attempt at a Solution [sin(xy) + xycos(xy)]dx = M(x,y) [1 +x^{2}cos(xy)dy = N(x,y) dM/dy sin(xy) = xcos(xy) xycos(xy) = uv' + vu' = (xy)(-xsin(xy)) + (x)(cos(xy)) u = xy du = x...

Homework Statement Use the integrating factor to solve the first order differential equation dy/dx + (2/x)y = 1 - 2/x subject to the initial condition y(1) = 2The Attempt at a Solution I have the full answer (it's an example), but my lecturer is notorious for omitting steps, to my constant...