(d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2+8x+9

解

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = x^{2} + 8 x + 9

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x ^{2}}{2} + \frac{11 x}{2} + \frac{49}{4}

解答ステップ

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = x^{2} + 8 x + 9

線形 ODE を解く:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x ^{2}}{2} + \frac{11 x}{2} + \frac{49}{4}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x ^{2}}{2} + \frac{11 x}{2} + \frac{49}{4}