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人気のある微分積分 >

(dy)/(dx)=((e^{x-y}))/(1+e^x),y(1)=0

解

\frac{d y}{d x} = \frac{( e ^{x - y} )}{1 + e ^{x}}, y (1) = 0

解

y = ln (ln (1 + e^{x}) + 1 - ln (1 + e))

解答ステップ

\frac{d y}{d x} = \frac{( e ^{x - y} )}{1 + e ^{x}}

分離可能 ODE を解く:

y = ln (ln (1 + e^{x}) + 1 - ln (1 + e))

y = ln (ln (1 + e^{x}) + 1 - ln (1 + e))

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