(d^2y)/(dx^2)+25y=5x^2+x

解

\frac{d ^{2} y}{d x ^{2}} + 25 y = 5 x^{2} + x

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

解答ステップ

\frac{d ^{2} y}{d x ^{2}} + 25 y = 5 x^{2} + x

線形 ODE を解く:

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

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