y^{''}+y^'-6y=-3sin(x)+4e^{2x}

解答

y^{^{''}} + y^{^{'}} - 6 y = - 3 sin (x) + 4 e^{2 x}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + \frac{21}{50} sin (x) + \frac{3}{50} cos (x) + \frac{4 e ^{2 x} x}{5}

求解步骤

y^{''} (x) + y^{'} (x) - 6 y = - 3 sin (x) + 4 e^{2 x}

求解线性方程:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + \frac{21}{50} sin (x) + \frac{3}{50} cos (x) + \frac{4 e ^{2 x} x}{5}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} + \frac{21}{50} sin (x) + \frac{3}{50} cos (x) + \frac{4 e ^{2 x} x}{5}