(D^2+4)y=sinh(x)sin(2x)

解

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ^{2} ( 2 x ) sinh ( x )}{2} d x + \frac{1}{68} sin (2 x) (- 4 sinh (x) cos (4 x) + cosh (x) sin (4 x))

解答ステップ

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

線形 ODE を解く:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ^{2} ( 2 x ) sinh ( x )}{2} d x + \frac{1}{68} sin (2 x) (- 4 sinh (x) cos (4 x) + cosh (x) sin (4 x))

y = c_{1} cos (2 x) + c_{2} sin (2 x) + cos (2 x) \cdot \int - \frac{sin ^{2} ( 2 x ) sinh ( x )}{2} d x + \frac{1}{68} sin (2 x) (- 4 sinh (x) cos (4 x) + cosh (x) sin (4 x))