4y^{''}-y=e^{x/2}x

解

4 y^{^{''}} - y = e^{\frac{x}{2}} x

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{\frac{x}{2}} x ^{2}}{8} + \frac{- e ^{\frac{x}{2}} x + e ^{\frac{x}{2}}}{4}

解答ステップ

4 y^{''} (x) - y = e^{\frac{x}{2}} x

線形 ODE を解く:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{\frac{x}{2}} x ^{2}}{8} + \frac{- e ^{\frac{x}{2}} x + e ^{\frac{x}{2}}}{4}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{\frac{x}{2}} x ^{2}}{8} + \frac{- e ^{\frac{x}{2}} x + e ^{\frac{x}{2}}}{4}