I would like to solve the following nonlinear ode, analytically
$\left(\frac{d^{2}u}{dt^{2}}\right)^{2}+\sin\left(\frac{du}{dt}\right)-\left(\frac{du}{dt}\right)^{\frac{1}{2}}-u-\cos\omega t=0$
Is there a way this can be transformed to linear equation(s), maybe using Fourier transform?