separable variables

w'=aw^2/3 ; w(0)=4

My work:

dw/dt=aw^2/3

dw=aw^2/3 dt

dw/w^2/3 = adt

int w^-2/3 dw = int a dt

3w^1/3 = at + C

w^1/3 = (at+c)/3

w=((at+c)/3)^3

w(0)=4=((a*0 + C)/3)^3

4=(C/3)^3

12=C^3 ...?

Think I messed up a while ago