y^{''}+153.06y^'+12739.6y=191094.97

解

y^{^{''}} + 153.06 y^{^{'}} + 12739.6 y = 191094.97

y = e^{- \frac{7653 t}{100}} (c_{1} cos (\frac{275310364 t}{200}) + c_{2} sin (\frac{275310364 t}{200})) + \frac{19109497}{1273960}

解答ステップ

y^{''} (t) + 153.06 y^{'} (t) + 12739.6 y = 191094.97

線形 ODE を解く:

y = e^{- \frac{7653 t}{100}} (c_{1} cos (\frac{275310364 t}{200}) + c_{2} sin (\frac{275310364 t}{200})) + \frac{19109497}{1273960}

y = e^{- \frac{7653 t}{100}} (c_{1} cos (\frac{275310364 t}{200}) + c_{2} sin (\frac{275310364 t}{200})) + \frac{19109497}{1273960}