2y^{''}+18y=3tan(3x)

解

2 y^{^{''}} + 18 y = 3 tan (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{- 2 cos ( 3 x ) ( ln ( tan ( 3 x ) + sec ( 3 x ) ) - sin ( 3 x ) ) - sin ( 6 x )}{12}

解答ステップ

2 y^{''} (x) + 18 y = 3 tan (3 x)

線形 ODE を解く:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{- 2 cos ( 3 x ) ( ln ( tan ( 3 x ) + sec ( 3 x ) ) - sin ( 3 x ) ) - sin ( 6 x )}{12}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{- 2 cos ( 3 x ) ( ln ( tan ( 3 x ) + sec ( 3 x ) ) - sin ( 3 x ) ) - sin ( 6 x )}{12}