36y^{''}-y=(xe^x)/6

解

36 y^{^{''}} - y = \frac{x e ^{x}}{6}

y = c_{1} e^{\frac{x}{6}} + c_{2} e^{- \frac{x}{6}} + \frac{e ^{x} x}{210} - \frac{12}{1225} e^{x}

解答ステップ

36 y^{''} (x) - y = \frac{x e ^{x}}{6}

線形 ODE を解く:

y = c_{1} e^{\frac{x}{6}} + c_{2} e^{- \frac{x}{6}} + \frac{e ^{x} x}{210} - \frac{12}{1225} e^{x}

y = c_{1} e^{\frac{x}{6}} + c_{2} e^{- \frac{x}{6}} + \frac{e ^{x} x}{210} - \frac{12}{1225} e^{x}