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人気のある微分積分 >

(1+t^2)y^'+4ty=(1+t^2)^{-2}

解

(1 + t^{2}) y^{^{'}} + 4 t y = (1 + t^{2})^{- 2}

解

y = \frac{arctan ( t )}{1 + 2 t ^{2} + t ^{4}} + \frac{c _{1}}{1 + 2 t ^{2} + t ^{4}}

解答ステップ

(1 + t^{2}) y^{'} (t) + 4 t y = (1 + t^{2})^{- 2}

線形 ODE を解く:

y = \frac{arctan ( t )}{1 + 2 t ^{2} + t ^{4}} + \frac{c _{1}}{1 + 2 t ^{2} + t ^{4}}

y = \frac{arctan ( t )}{1 + 2 t ^{2} + t ^{4}} + \frac{c _{1}}{1 + 2 t ^{2} + t ^{4}}

グラフ

人気の例

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