(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the general solution of each homogeneous equation.

2. Relevant equations

(x^2)y'=2(y^2)-x^2

3. The attempt at a solution

Because y'=(dy/dx), I changed the equation to (x^2-2y^2)dx+x^2dy=0

Homogeneous of degree is 2.

I let y=xv, dy=vdx+xdv

So, I have (x^2-2x^2v^2)dx+x^2(vdx+xdv)=0

This equals to (1-2v^2+v)dx+xdv=0

Then, the integrating factor is 1/x(1-2v^2+v)

so, dx/x+dv/1-2^2+v=0

Here, I need to integrate dv/1-2v^2+v, but I don't how to do it.

So, does anyone help me calculate it? or if you find any mistake in my work, please please let me know.

Thank you so much.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Homemogeneous Equation

**Physics Forums | Science Articles, Homework Help, Discussion**