calc problem differencial equation

hi, i was wondering if i did this problem right. i had to solve the following differential equation for y as a function of t using separation of variables:

y' = yt^2

so this is what i did.

i set dy/dt = yt^2

then from that i got dy/y = t^2 dt, which is the same as 1/y dy = t^2 dt.

i took the integral of both sides.

the integral of 1/y dy is ln(y)

the integral of t^2 dt is t^3/3 + C

so then i got that y = e^(ln(t^3/3)+C)

this is the same as y = e^(ln(t^3/3) * e^C

then i got y = (t^3 * e^c)/3 for a final answer.