- #1
peace-Econ
- 34
- 0
Homework Statement
Find the general solution of each homogeneous equation.
Homework Equations
(x^2)y'=2(y^2)-x^2
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.