What is the solution for (1+e^x)(dy}{dx}=\frac{e^x)/y ?

The solution for (1+e^x)(dy}{dx}=\frac{e^x)/y is y=sqrt(2ln(1+e^x)+c_{1)},y=-sqrt(2ln(1+e^x)+c_{1)}

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(1+e^x)(dy}{dx}=\frac{e^x)/y

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

y = 2 ln (1 + e^{x}) + c_{1}, y = - 2 ln (1 + e^{x}) + c_{1}

Solution steps

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

Solve separable ODE:

y = 2 ln (1 + e^{x}) + c_{1}, y = - 2 ln (1 + e^{x}) + c_{1}

y = 2 ln (1 + e^{x}) + c_{1}, y = - 2 ln (1 + e^{x}) + c_{1}

\frac{d y}{d x} = x y + x - 2 y - 2, a y (0) = 2

y^{^{'}} = (\frac{2 - e ^{x}}{3 + 2 y})

6 x - 8 y x^{2} + 1 y^{^{'}} = 0

y^{^{'}} + y = x y

1000 y^{^{'}} = 5000 - 100 y

What is the solution for (1+e^x)(dy}{dx}=\frac{e^x)/y ?
The solution for (1+e^x)(dy}{dx}=\frac{e^x)/y is y=sqrt(2ln(1+e^x)+c_{1)},y=-sqrt(2ln(1+e^x)+c_{1)}