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

The solution for (1+ln(x)+y/x)dx-(1-ln(x))dy=0 is y=(xln(x))/(1-ln(x))+(c_{1})/(1-ln(x))

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

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

y = \frac{x ln ( x )}{1 - ln ( x )} + \frac{c _{1}}{1 - ln ( x )}

Solution steps

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

Solve linear ODE:

y = \frac{x ln ( x )}{1 - ln ( x )} + \frac{c _{1}}{1 - ln ( x )}

y = \frac{x ln ( x )}{1 - ln ( x )} + \frac{c _{1}}{1 - ln ( x )}

\frac{d y}{d x} = 2 x + y

y^{^{'}} + 2 x y = 0, y (0) = 3

\int sec^{6} (x) tan^{6} (x) d x

ln (x^{4} + 3)

\int_{0}^{1} 2 π (x) (e^{- x^{2}}) d x

What is the solution for (1+ln(x)+y/x)dx-(1-ln(x))dy=0 ?
The solution for (1+ln(x)+y/x)dx-(1-ln(x))dy=0 is y=(xln(x))/(1-ln(x))+(c_{1})/(1-ln(x))