(d^2x)/(dt^2)+16x=1+2sin(4t)

解

\frac{d ^{2} x}{d t ^{2}} + 16 x = 1 + 2 sin (4 t)

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{16} - \frac{t cos ( 4 t )}{4}

解答ステップ

\frac{d ^{2} x}{d t ^{2}} + 16 x = 1 + 2 sin (4 t)

線形 ODE を解く:

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{16} - \frac{t cos ( 4 t )}{4}

x = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{16} - \frac{t cos ( 4 t )}{4}