Seperable differential equations question

[csc2iffy]

Homework Statement

Solve the differential equation dy/dx = 3x²(1+y²)^3/2

Homework Equations

The Attempt at a Solution

So far this is what I have (I'm almost finished) -

∫dy/(1+y)^3/2 = ∫3x² dx
Let y = tan(u) , dy = sec²(u)
Then (1+y²)^3/2 = (tan²(u)+1)^3/2 = sec³(u) and u = tan^-1(y)
∫cos(u)du = ∫3x²dx
sin(u)+c = x³+c
sin(tan^-1(y)) = x³+C

One question here, how do I simplify the left-hand side? I seem to have forgotten. Thanks!

 

[Dick]

Draw a right triangle with an angle 'a' that satisfies tan(a)=y. Work out the hypotenuse. Now find sin(a).

 

[csc2iffy]

thank you!