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

解答

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}

求解步骤

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

求解线性方程:

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}

\frac{d ^{3} y}{d x ^{3}} + y = e^{- x} + 1

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 20 y = e^{- 5 x}

y^{^{''}} - y^{^{'}} - 16 = 0

y^{^{''}} + 40 y^{^{'}} + 6250 y = 100 cos (10 t)

y^{^{''}} + 2 y^{^{'}} + 2 y = e - x cos (x)