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人気のある微分積分 >

x^'+2/(1+t)x=(e^t)/(1+t)

解

x^{^{'}} + \frac{2}{1 + t} x = \frac{e ^{t}}{1 + t}

解

x = \frac{e ^{t} t}{1 + 2 t + t ^{2}} + \frac{c _{1}}{1 + 2 t + t ^{2}}

解答ステップ

x^{'} (t) + \frac{2}{1 + t} x = \frac{e ^{t}}{1 + t}

線形 ODE を解く:

x = \frac{e ^{t} t}{1 + 2 t + t ^{2}} + \frac{c _{1}}{1 + 2 t + t ^{2}}

x = \frac{e ^{t} t}{1 + 2 t + t ^{2}} + \frac{c _{1}}{1 + 2 t + t ^{2}}

グラフ

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