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人気のある微分積分 >

y^{''}-5y^'+4y=5sin(5t)

解

y^{^{''}} - 5 y^{^{'}} + 4 y = 5 sin (5 t)

解

y = c_{1} e^{4 t} + c_{2} e^{t} - \frac{105}{1066} sin (5 t) + \frac{125}{1066} cos (5 t)

解答ステップ

y^{''} (t) - 5 y^{'} (t) + 4 y = 5 sin (5 t)

線形 ODE を解く:

y = c_{1} e^{4 t} + c_{2} e^{t} - \frac{105}{1066} sin (5 t) + \frac{125}{1066} cos (5 t)

y = c_{1} e^{4 t} + c_{2} e^{t} - \frac{105}{1066} sin (5 t) + \frac{125}{1066} cos (5 t)

グラフ

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