(d^2+4)y=x^2sin(2x)

解

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{3} cos ( 2 x )}{12} + \frac{x ^{2} sin ( 2 x )}{16} + \frac{x cos ( 2 x )}{32}

解答ステップ

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

線形 ODE を解く:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{3} cos ( 2 x )}{12} + \frac{x ^{2} sin ( 2 x )}{16} + \frac{x cos ( 2 x )}{32}

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{3} cos ( 2 x )}{12} + \frac{x ^{2} sin ( 2 x )}{16} + \frac{x cos ( 2 x )}{32}