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人気のある微分積分 >

y^{''}-3y^'+7y=4e^{3t}

解

y^{^{''}} - 3 y^{^{'}} + 7 y = 4 e^{3 t}

解

y = e^{\frac{3 t}{2}} (c_{1} cos (\frac{19 t}{2}) + c_{2} sin (\frac{19 t}{2})) + \frac{4}{7} e^{3 t}

解答ステップ

y^{''} (t) - 3 y^{'} (t) + 7 y = 4 e^{3 t}

線形 ODE を解く:

y = e^{\frac{3 t}{2}} (c_{1} cos (\frac{19 t}{2}) + c_{2} sin (\frac{19 t}{2})) + \frac{4}{7} e^{3 t}

y = e^{\frac{3 t}{2}} (c_{1} cos (\frac{19 t}{2}) + c_{2} sin (\frac{19 t}{2})) + \frac{4}{7} e^{3 t}

グラフ

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