Originally Posted by
skirk34 Any help solving homogenous differntial equation would be greatly appreciated:
dy/dx=(-2x^2+2y^2)/xy
The following is what i've worked out (could be incorrect):
dy/dx=2(y/x-x/y)
let v=y/x, dy/dx=v+x*dv/dx
v+x*dv/dx=2(v-1/v), x*dv/dx=2(v-1/v)-v
therefore, x*dv/dx=(v^2-2)/v
1/x dx=v/(v^2-2) dv
-ln(x)+C=1/2 ln(v^2-2)
C/x=1/2(y^2/x^2-2)
C/x=y^2/2x^2-1
C/x+1=y^2/2x^2
y^2=2x^2(C/x+1)
y=sqrt(2x^2(C/x+1))
I must of gone wrong somewhere as it says the answer is incorrect, i dont know where though...