Integrating factor Definition and 123 Threads

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...

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...

I'm solving the following equation in the unit square using finite differences: epsilon(u_xx+u_yy)+u_x+u_y=0, where epsilon is a singular perturbation parameter. I need to use domain decomposition to isolate the corner singularity in the outflow corner. My subdomain in this corner is a...

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...