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人気のある微分積分 >

(1-x^2)y^'=1

解

(1 - x^{2}) y^{^{'}} = 1

解

y = \frac{ln ( x + 1 )}{2} - \frac{ln ( x - 1 )}{2} + c_{1}

解答ステップ

(1 - x^{2}) y^{'} (x) = 1

分離する

y^{'} (x) : y^{'} (x) = \frac{1}{1 - x ^{2}}

f^{^{'}} (x) = g (x)

であれば

f (x) = \int g (x) d x

y = \int \frac{1}{1 - x ^{2}} d x

\int \frac{1}{1 - x ^{2}} d x = \frac{ln ( x + 1 )}{2} - \frac{ln ( x - 1 )}{2} + c_{1}

y = \frac{ln ( x + 1 )}{2} - \frac{ln ( x - 1 )}{2} + c_{1}

グラフ

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