Question

Solve the seperable equation:
dx/dt=3xt^2

Answer 1

`\displaystyle (dx)/(dt)=3xt^2\\ (dx)/(x)=3t^2 \, dt\\ \int (dx)/(x)=\int 3t^2 \, dt\\ \ln x=3(t^3)/(3)+C\\ \ln x=t^3+C\\ x=e^(t^3+C)\\ x=e^(t^3)\cdot e^C\\ \boxed{x=Ce^(t^3)}`