(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.

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# Homemogeneous Equation

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