(d^2y)/(dx^2)-5(dy)/(dx)+8y=xe^x

解

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 8 y = x e^{x}

y = e^{\frac{5 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{4} + \frac{3}{16} e^{x}

解答ステップ

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 8 y = x e^{x}

線形 ODE を解く:

y = e^{\frac{5 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{4} + \frac{3}{16} e^{x}

y = e^{\frac{5 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{4} + \frac{3}{16} e^{x}