Question

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

Answer 1

$\displaystyle \dfrac{dx}{dt}=3xt^2\\ \dfrac{dx}{x}=3t^2 \, dt\\ \int \dfrac{dx}{x}=\int 3t^2 \, dt\\ \ln x=3\dfrac{t^3}{3}+C\\ \ln x=t^3+C\\ x=e^{t^3+C}\\ x=e^{t^3}\cdot e^C\\ \boxed{x=Ce^{t^3}}$