(d^2-2d+2)y=(x+e^x)sin(x)

解

(d^{2} - 2 d + 2) y = (x + e^{x}) sin (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{x sin ( x ) + 2 x cos ( x )}{5} + \frac{2}{25} sin (x) + \frac{14}{25} cos (x) - \frac{e ^{x} x cos ( x )}{2}

解答ステップ

(d^{2} - 2 d + 2) y = (x + e^{x}) sin (x)

線形 ODE を解く:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{x sin ( x ) + 2 x cos ( x )}{5} + \frac{2}{25} sin (x) + \frac{14}{25} cos (x) - \frac{e ^{x} x cos ( x )}{2}

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{x sin ( x ) + 2 x cos ( x )}{5} + \frac{2}{25} sin (x) + \frac{14}{25} cos (x) - \frac{e ^{x} x cos ( x )}{2}