End of differential equation, quick alegbra Q

[csc2iffy]

Homework Statement

I just solved a differential equation and got the problem down to its implicit solution:
y/√(1+y²) = x³+C where C is an arbitrary constant
My question now is, how can I solve for y? I can't get past the algebra. Thanks!

Homework Equations

The Attempt at a Solution

 

[Dick]

Square both sides. Solve for y^2. Take a square root. Come on. Try it.

 

[ashwinnarayan]

Square both sides and bring the bottom part to the other side. You'll get

$y^2 = (1+y^2)(x^3 + c)^2$

Then multiply out and regroup.

$y^2 -y^2(x^3 + c)^2 = (x^3 + c)^2$

then you'll get $y^2 = \frac{(x^3+c)^2}{1-(x^3+c)^2}$

So $y = \sqrt{\frac{(x^3+c)^2}{1-(x^3+c)^2}}$

 

[csc2iffy]

thank you!