Separate Variables Differential Eq. of Cubic Power

1. Jun 4, 2013

knowLittle

1. The problem statement, all variables and given/known data
When possible express the general solution in explicit form.
Solve dy/dx =x^2 /(1+y^2)

2. Relevant equations
This is a first order non-linear ordinary differential equation.

3. 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

Thank you.

2. Jun 4, 2013

Dick

I really don't think you want to solve for y. With an expression like that I'd just leave in the implicit form you already have, or maybe express x as a function of y instead. Don't try to use the cubic formula. It's a mess.

Last edited: Jun 4, 2013
3. Jun 4, 2013

knowLittle

Yes, I am aware that it is kinda difficult to solve for 'y' and that's why I wanted to try it out. It involves imaginary numbers and many roots.
If someone can point me in the right direction, that would great.

4. Jun 4, 2013

YawningDog27

Luckily, this is a seperable equation, which means you can rewrite it as
$$(1+y^2)dy = x^2dx.$$
Now, what can you do to get rid of those pesky differentials?

5. Jun 4, 2013

6. Jun 4, 2013

knowLittle

Thank you, tiny-tim. I usually use latex for big equations, but I thought it wouldn't be a big deal.

I was thinking that I could solve it like your wikipedia link... this will be interesting. Thanks.

7. Jun 4, 2013

Staff: Mentor

You really need to read through the thread. The OP has already done this and has gotten a solution.