y^{''}+y^'-2y=e^xsin(x/2)cos(x/2)

解

y^{^{''}} + y^{^{'}} - 2 y = e^{x} sin (\frac{x}{2}) cos (\frac{x}{2})

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{e ^{x} ( 3 cos ( x ) + sin ( x ) )}{20}

解答ステップ

y^{''} (x) + y^{'} (x) - 2 y = e^{x} sin (\frac{x}{2}) cos (\frac{x}{2})

線形 ODE を解く:

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{e ^{x} ( 3 cos ( x ) + sin ( x ) )}{20}

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{e ^{x} ( 3 cos ( x ) + sin ( x ) )}{20}