Solve the separable differential equation dzdθ=θ3\frac{dz}{d\theta} = \theta^3dθdz=θ3 for z(θ)z(\theta)z(θ).
z=θ44+Cz = \frac{\theta^4}{4} + Cz=4θ4+C
z=θ4+Cz = \theta^4 + Cz=θ4+C
z=3θ2+Cz = 3\theta^2 + Cz=3θ2+C
z=θ33+Cz = \frac{\theta^3}{3} + Cz=3θ3+C