(d^2y)/(dx^2)-5(dy)/(dx)+6y=x^3+2x^2+5x+2

解

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{3} + 2 x^{2} + 5 x + 2

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{3 x ^{2}}{4} + \frac{23 x}{12} + \frac{121}{72}

解答ステップ

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{3} + 2 x^{2} + 5 x + 2

線形 ODE を解く:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{3 x ^{2}}{4} + \frac{23 x}{12} + \frac{121}{72}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{3 x ^{2}}{4} + \frac{23 x}{12} + \frac{121}{72}