When possible express the general solution in explicit form.
Solve dy/dx =x^2 /(1+y^2)
This is a first order non-linear ordinary differential equation.
The Attempt at a Solution
dy(1+y^2) = x^2 dx
Integration both sides returns:
y+ (y^3 )/3= (x^3)/3 +C
Now, I am aware that there is more than one solution for y involving imaginary numbers. Can someone help me in the next step or direct me to a site?
I have seen cubic solutions tutorial, but they involve equations of the form: Ax^3+Bx^2+Cx+D=0