(d^2y)/(dx^2)-2(dy)/(dx)+5y=x^3

解

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 5 y = x^{3}

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{3}}{5} + \frac{6 x ^{2}}{25} - \frac{6 x}{125} - \frac{72}{625}

解答ステップ

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 5 y = x^{3}

線形 ODE を解く:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{3}}{5} + \frac{6 x ^{2}}{25} - \frac{6 x}{125} - \frac{72}{625}

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{3}}{5} + \frac{6 x ^{2}}{25} - \frac{6 x}{125} - \frac{72}{625}