y^{''}+100y=-2sin(10t)-4cos(10t)

解

y^{^{''}} + 100 y = - 2 sin (10 t) - 4 cos (10 t)

y = c_{1} cos (10 t) + c_{2} sin (10 t) - \frac{t sin ( 10 t )}{5} + \frac{t cos ( 10 t )}{10}

解答ステップ

y^{''} (t) + 100 y = - 2 sin (10 t) - 4 cos (10 t)

線形 ODE を解く:

y = c_{1} cos (10 t) + c_{2} sin (10 t) - \frac{t sin ( 10 t )}{5} + \frac{t cos ( 10 t )}{10}

y = c_{1} cos (10 t) + c_{2} sin (10 t) - \frac{t sin ( 10 t )}{5} + \frac{t cos ( 10 t )}{10}