What is the solution for x(y+1)dx+y(x-1)dy=0 ?

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

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x(y+1)dx+y(x-1)dy=0

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

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

Solution steps

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

x \to 0 lim (\frac{x}{x ^{2} - 1})

\frac{d}{d x} (\frac{1}{x ( ln ( x ) )})

81 y^{^{''}} + 108 y^{^{'}} + 66 y = 0, y^{^{'}} (0) = 2, y (0) = 6

1 - x

\frac{d}{d x} (\frac{9 x}{64 + x ^{2} + y ^{2}})

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