y^{''}+4y=9sec(2x)

解

y^{^{''}} + 4 y = 9 sec (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{9}{4} ln (cos (2 x)) cos (2 x) + \frac{9}{2} x sin (2 x)

解答ステップ

y^{''} (x) + 4 y = 9 sec (2 x)

線形 ODE を解く:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{9}{4} ln (cos (2 x)) cos (2 x) + \frac{9}{2} x sin (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{9}{4} ln (cos (2 x)) cos (2 x) + \frac{9}{2} x sin (2 x)