2y^{''}+12y=6tan(3x)

解

2 y^{^{''}} + 12 y = 6 tan (3 x)

y = c_{1} cos (6 x) + c_{2} sin (6 x) + cos (6 x) \cdot \int - \frac{6 sin ( 6 x ) tan ( 3 x )}{2} d x + sin (6 x) \cdot \int \frac{6 cos ( 6 x ) tan ( 3 x )}{2} d x

解答ステップ

2 y^{''} (x) + 12 y = 6 tan (3 x)

線形 ODE を解く:

y = c_{1} cos (6 x) + c_{2} sin (6 x) + cos (6 x) \cdot \int - \frac{6 sin ( 6 x ) tan ( 3 x )}{2} d x + sin (6 x) \cdot \int \frac{6 cos ( 6 x ) tan ( 3 x )}{2} d x

y = c_{1} cos (6 x) + c_{2} sin (6 x) + cos (6 x) \cdot \int - \frac{6 sin ( 6 x ) tan ( 3 x )}{2} d x + sin (6 x) \cdot \int \frac{6 cos ( 6 x ) tan ( 3 x )}{2} d x