(d^2+4)y=sin^3(x)

解

(d^{2} + 4) y = sin^{3} (x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{5} sin^{5} (x) cos (2 x) + sin (2 x) \cdot \int \frac{sin ^{3} ( x ) cos ( 2 x )}{2} d x

解答ステップ

(d^{2} + 4) y = sin^{3} (x)

線形 ODE を解く:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{5} sin^{5} (x) cos (2 x) + sin (2 x) \cdot \int \frac{sin ^{3} ( x ) cos ( 2 x )}{2} d x

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{5} sin^{5} (x) cos (2 x) + sin (2 x) \cdot \int \frac{sin ^{3} ( x ) cos ( 2 x )}{2} d x