4y^{''}+36y=csc(x)

解

4 y^{^{''}} + 36 y = csc (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + cos (3 x) \cdot \int - \frac{3 - 4 sin ^{2} ( x )}{12} d x + sin (3 x) \cdot \int \frac{csc ( x ) cos ( 3 x )}{12} d x

解答ステップ

4 y^{''} (x) + 36 y = csc (x)

線形 ODE を解く:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + cos (3 x) \cdot \int - \frac{3 - 4 sin ^{2} ( x )}{12} d x + sin (3 x) \cdot \int \frac{csc ( x ) cos ( 3 x )}{12} d x

y = c_{1} cos (3 x) + c_{2} sin (3 x) + cos (3 x) \cdot \int - \frac{3 - 4 sin ^{2} ( x )}{12} d x + sin (3 x) \cdot \int \frac{csc ( x ) cos ( 3 x )}{12} d x