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

解

(d^{3} - 3 d^{2} + 4 d - 2) \cdot y = e^{x} + cos (x) + x

y = c_{1} e^{x} + e^{x} (c_{2} cos (x) + c_{3} sin (x)) + e^{x} x + \frac{3}{10} sin (x) + \frac{1}{10} cos (x) - \frac{x}{2} - 1

解答ステップ

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

線形 ODE を解く:

y = c_{1} e^{x} + e^{x} (c_{2} cos (x) + c_{3} sin (x)) + e^{x} x + \frac{3}{10} sin (x) + \frac{1}{10} cos (x) - \frac{x}{2} - 1

y = c_{1} e^{x} + e^{x} (c_{2} cos (x) + c_{3} sin (x)) + e^{x} x + \frac{3}{10} sin (x) + \frac{1}{10} cos (x) - \frac{x}{2} - 1