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

解

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

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + \frac{1}{8} (x - \frac{1}{2} sin (2 x)) - \frac{1}{4} cos (2 x) (\frac{1}{2} sin^{2} (x) sin (2 x) - \frac{1}{4} (x - \frac{1}{4} sin (4 x))) - \frac{1}{8} sin^{4} (x) sin (2 x)

解答ステップ

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

線形 ODE を解く:

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + \frac{1}{8} (x - \frac{1}{2} sin (2 x)) - \frac{1}{4} cos (2 x) (\frac{1}{2} sin^{2} (x) sin (2 x) - \frac{1}{4} (x - \frac{1}{4} sin (4 x))) - \frac{1}{8} sin^{4} (x) sin (2 x)

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + \frac{1}{8} (x - \frac{1}{2} sin (2 x)) - \frac{1}{4} cos (2 x) (\frac{1}{2} sin^{2} (x) sin (2 x) - \frac{1}{4} (x - \frac{1}{4} sin (4 x))) - \frac{1}{8} sin^{4} (x) sin (2 x)