(d^2-8d+20)y=100x^2-26xe^x

解

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

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10} - 2 x e^{x} - \frac{12}{13} e^{x}

解答ステップ

(d^{2} - 8 d + 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} - 2 x e^{x} - \frac{12}{13} e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10} - 2 x e^{x} - \frac{12}{13} e^{x}