What is the solution for (1+y)xdx-(1+x)ydy=0 ?

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

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(1+y)xdx-(1+x)ydy=0

(1 + y) x d x - (1 + x) y d y = 0

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

Solution steps

(1 + y) x d x - (1 + x) y d y = 0

Solve separable ODE:

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

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

\int \frac{1}{( 1 + 4 y ^{2} )} d y

\frac{d}{d x} (e^{- \frac{1}{2} x})

\frac{3 e ^{- 7 s}}{s ^{2}} + \frac{7 e ^{- 7 s}}{s} + \frac{2 e ^{- 7 s}}{s}

\int 2 x e^{- 2 x} d x

\frac{d}{d x} (\frac{x ^{3} + 5}{x ^{2} + 2 x + 3})

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