What is the solution for ((2xy+1))/y dx+((y-x))/(y^2)dy=0 ?

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

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((2xy+1))/y dx+((y-x))/(y^2)dy=0

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

y = - \frac{x}{W ( - \frac{x}{e ^{c_{1} - x^{2}}} )}

Solution steps

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

Solve using substitution:

y = - \frac{x}{W ( - \frac{x}{e ^{c_{1} - x^{2}}} )}

y = - \frac{x}{W ( - \frac{x}{e ^{c_{1} - x^{2}}} )}

sin (sin (x))

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