Solve the separable equation dzdθ=θ⋅z\frac{dz}{d\theta} = \theta \cdot zdθdz=θ⋅z for zzz.
z=Ceθ2z = Ce^{\theta^2}z=Ceθ2
z=Ce12θ2z = Ce^{\frac{1}{2}\theta^2}z=Ce21θ2
z=12θ2+Cz = \frac{1}{2}\theta^2 + Cz=21θ2+C
z=Ceθz = Ce^{\theta}z=Ceθ