Solve-for-u-and-v-in-the-system-of-equations-below-u-e-2x-cos2x-v-e-2x-sin2x-0-u-e-2x-cos2x-v-e-2x-sin2x-xe-2x-sinx-where-u-and-v-are-functions-of-x-

Question Number 108180 by Ar Brandon last updated on 15/Aug/20

Solve for u and v in the system of equations below

{\begin{cases} u^{'} (e^{- 2 x} \cos 2 x) + v^{'} (e^{- 2 x} \sin 2 x) = 0 \\ u^{'} {(e^{- 2 x} \cos 2 x)}^{'} + v^{'} {(e^{- 2 x} \sin 2 x)}^{'} = {xe}^{- 2 x} sinx \end{cases}

where u and v are functions of x