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.