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人気のある微分積分 >

y^{''}-3y^'+2y=2t^3

解

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 t^{3}

解

y = c_{1} e^{2 t} + c_{2} e^{t} + t^{3} + \frac{9 t ^{2}}{2} + \frac{21 t}{2} + \frac{45}{4}

解答ステップ

y^{''} (t) - 3 y^{'} (t) + 2 y = 2 t^{3}

線形 ODE を解く:

y = c_{1} e^{2 t} + c_{2} e^{t} + t^{3} + \frac{9 t ^{2}}{2} + \frac{21 t}{2} + \frac{45}{4}

y = c_{1} e^{2 t} + c_{2} e^{t} + t^{3} + \frac{9 t ^{2}}{2} + \frac{21 t}{2} + \frac{45}{4}

グラフ

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