(d^2+1)y=sin(x)sin^2(x)

解

(d^{2} + 1) y = sin (x) sin^{2} (x)

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) (\frac{1}{4} sin^{3} (x) cos (x) - \frac{3}{8} x + \frac{3}{16} sin (2 x)) + \frac{sin ^{5} ( x )}{4}

解答ステップ

(d^{2} + 1) y = sin (x) sin^{2} (x)

線形 ODE を解く:

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) (\frac{1}{4} sin^{3} (x) cos (x) - \frac{3}{8} x + \frac{3}{16} sin (2 x)) + \frac{sin ^{5} ( x )}{4}

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) (\frac{1}{4} sin^{3} (x) cos (x) - \frac{3}{8} x + \frac{3}{16} sin (2 x)) + \frac{sin ^{5} ( x )}{4}