(d^4-2d^3+d^2)y=x^3

解

(d^{4} - 2 d^{3} + d^{2}) y = x^{3}

y = c_{1} + c_{2} x + c_{3} e^{x} + c_{4} x e^{x} + \frac{x ^{5}}{20} + \frac{x ^{4}}{2} + 3 x^{3} + 12 x^{2}

解答ステップ

(d^{4} - 2 d^{3} + d^{2}) y = x^{3}

線形 ODE を解く:

y = c_{1} + c_{2} x + c_{3} e^{x} + c_{4} x e^{x} + \frac{x ^{5}}{20} + \frac{x ^{4}}{2} + 3 x^{3} + 12 x^{2}

y = c_{1} + c_{2} x + c_{3} e^{x} + c_{4} x e^{x} + \frac{x ^{5}}{20} + \frac{x ^{4}}{2} + 3 x^{3} + 12 x^{2}