Homework Help: Is this general solution for ODE correct?

Find the general solution of the following ODE:

dx/dt = 3x^(2) cos t



Make x the subject of the solution.



Heres my solution, is this correct?

dx/dt = 3x^(2) cos t

dx/3x^(2) = cos t dt

Integrating both sides gives:

ln (3x^(2)) = sin t + C

3x^(2) = e^(sin t + C)

3x^(2) = Ae^(sin t)

x^(2) = (Ae^(sin t))/3)

x = SQRT(Ae^(sin t))/3)
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

 

So from what you have said:

∫dx/3x^(2) = -1/3x + C or (-x^(-1)/3) + C

Giving a solution of:

-1/3x + C = sin t