What is the solution for e^{x/2}ydy-(dx)/(e^y(1+e^{x/2))}=0 ?

The solution for e^{x/2}ydy-(dx)/(e^y(1+e^{x/2))}=0 is y=\W((-x-2e^{-x/2}+2ln(e^{x/2}+1)+c_{1})/e)+1

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e^{x/2}ydy-(dx)/(e^y(1+e^{x/2))}=0

e^{\frac{x}{2}} y d y - \frac{d x}{e ^{y} ( 1 + e ^{\frac{x}{2}} )} = 0

y = W (\frac{- x - 2 e ^{- \frac{x}{2}} + 2 ln ( e ^{\frac{x}{2}} + 1 ) + c _{1}}{e}) + 1

Solution steps

e^{\frac{x}{2}} y d y - \frac{d x}{e ^{y} ( 1 + e ^{\frac{x}{2}} )} = 0

Solve separable ODE:

y = W (\frac{- x - 2 e ^{- \frac{x}{2}} + 2 ln ( e ^{\frac{x}{2}} + 1 ) + c _{1}}{e}) + 1

y = W (\frac{- x - 2 e ^{- \frac{x}{2}} + 2 ln ( e ^{\frac{x}{2}} + 1 ) + c _{1}}{e}) + 1

\frac{d V}{d x} = - 0.4 V

3 N^{^{'}} + 4 t N^{6} = 0

y^{^{'}} + k y = c

x^{^{'}} = x^{2} + x + 1

(y x^{2} - y) d y = arctan (x) d x

What is the solution for e^{x/2}ydy-(dx)/(e^y(1+e^{x/2))}=0 ?
The solution for e^{x/2}ydy-(dx)/(e^y(1+e^{x/2))}=0 is y=\W((-x-2e^{-x/2}+2ln(e^{x/2}+1)+c_{1})/e)+1