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

$$\mathrm{Solve}\mathrm{for}\mathrm{u}\mathrm{and}\mathrm{v}\mathrm{in}\mathrm{the}\mathrm{system}\mathrm{of}\mathrm{equations}\mathrm{below}$$$$\{\begin{array}{l}{\mathrm{u}}^{\prime }\left({\mathrm{e}}^{-2\mathrm{x}}\cos 2\mathrm{x}\right)+{\mathrm{v}}^{\prime }\left({\mathrm{e}}^{-2\mathrm{x}}\sin 2\mathrm{x}\right)=0\\ {\mathrm{u}}^{\prime }{\left({\mathrm{e}}^{-2\mathrm{x}}\cos 2\mathrm{x}\right)}^{\prime }+{\mathrm{v}}^{\prime }{\left({\mathrm{e}}^{-2\mathrm{x}}\sin 2\mathrm{x}\right)}^{\prime }={\mathrm{xe}}^{-2\mathrm{x}}\mathrm{sinx}\end{array}$$$$\mathrm{where}\mathrm{u}\mathrm{and}\mathrm{v}\mathrm{are}\mathrm{functions}\mathrm{of}\mathrm{x}$$

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