Integrating factor Definition and 113 Threads

Got the eqn dy/dx=x(1-y) and it can be solved both linear and separable methods.(Linear method being using a integrating factor) Problem I am having is that with this two methods i get two different (yet similar answers) and was wondering if you can see my problem with this two methods I am...

Hi there, I am having a bit of difficulty finding the integration factor for the following problem. The problem lies in taking the integral of a function of two variables. Anyways, here's what I have: y^2+y-xy'=0 I then divided by x (i prefer it this way), so \frac{y^2+y}{x} + y' = 0 then...

What approach should be used to solve the following DE: dy/dx= (-2x+5y)/(2x+y) Find an integrating factor and solve it as an excact equation? Thanks.

Hello everyone I understand how to solve exact equations, but what happens when they arnt' exact? I'm confused on what I'm suppose to do! Does anyone feel like explaning hte process to me, if given an integrating factor/> or give me a website? Here is my problem: Check that the equation...

Hey everyone, I need to find an integrating factor of the form x^n*y^m, to solve a differential equation i have... however i do not know the process to solve for an integration of this form.. .any help?? Thanks Steph

for the equation, (a+1)ydx+(b+1)xdy=0, i am wondering how to get (x^a)(y^b) as an integrating factor~ the following is my work: (1/F)(dF/dx)=(a-b)/[(b+1)x] => F=cx^[(a-b)/(b+1)] why doesn't that method work?

for the question, siny+cosydy=0, i want to find an integrating factor. my work: (1/F)(dF/dx)=(1/cosy)(cosy+siny)=1+tany =>lny=x +xtany +c` => y =ce^(x+xtany) however, the question wants the integrating factor to be e^x... why?

Howdy, I've read this forum for some time, however this is my first post. I am attempting to solve this ODE. I am looking to find an integrating factor, then solve. I have attached the link to the problem set if my input here is ambiguous. Number 4d. Thank you kindly for any help you might...

Q. By finding a suitable integrating factor, solve the following equation: \left( {x + y^3 } \right)y' = y (treat y as the independent variable). Answer: Exact equation is y^{ - 1} \left( {\frac{{dx}}{{dy}}} \right) - xy^{ - 2} = y leading to x = y\left( {k + \frac{{y^2 }}{2}} \right)...

For eg is there a way to find IF for pydx +qxdy +x^my^n(rydx+sxdy)=0

Q. Motivate the Integrating factor strategy for U ( "Mew" ) of y I know how to prove it for "Mew" of x but how to do for "mew" of y Maybe something like this. Mdx (x.y) + Ndy ( x, y ) = 0 Assume this is differentiable so let us multiply by "mew" of x on both sides to make it...

Here's the problem: y\left( 2x-y-1 \right) dx + x\left( 2y-x-1 \right) dy = 0 So rewrite it as: \left( 2xy-y^2-y \right) dx + \left( 2xy-x^2-x \right) dy = 0 Now it's in the form,…P(x,y) dx + Q(x,y) dy = 0 \frac{\partial P(x,y)}{\partial y} = 2x-2y-1 \frac {\partial...

I am trying to solve a linear equation and getting stuck. y' + 2xy = x^2 I am using e^{x^2} as my integrating factor and multiplying that to both sides. Afterwards, I am able to wrap up the LHS as [y e^{x^2}]' and I have [y e^{x^2}]' = x^2 e^{x^2} Now all I need to do is...