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.