y^{''}+8y^'+20y=100x^2-26xe^x

解

y^{^{''}} + 8 y^{^{'}} + 20 y = 100 x^{2} - 26 x e^{x}

y = e^{- 4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} - 4 x + \frac{11}{10} - \frac{26 e ^{x} x}{29} + \frac{260}{841} e^{x}

解答ステップ

y^{''} (x) + 8 y^{'} (x) + 20 y = 100 x^{2} - 26 x e^{x}

線形 ODE を解く:

y = e^{- 4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} - 4 x + \frac{11}{10} - \frac{26 e ^{x} x}{29} + \frac{260}{841} e^{x}

y = e^{- 4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} - 4 x + \frac{11}{10} - \frac{26 e ^{x} x}{29} + \frac{260}{841} e^{x}