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=(1-ln(x))*integral of (-ln(x)-1)/((1-ln(x))^2)

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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 = (1 - ln (x)) \cdot \int \frac{- ln ( x ) - 1}{( 1 - ln ( x ) ) ^{2}} d x

Solution steps

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

Solve linear ODE:

y = (1 - ln (x)) \cdot \int \frac{- ln ( x ) - 1}{( 1 - ln ( x ) ) ^{2}} d x

y = (1 - ln (x)) \cdot \int \frac{- ln ( x ) - 1}{( 1 - ln ( x ) ) ^{2}} d x

\frac{d}{d t} (e^{2 t} \cdot y)

x \to 4 lim (\frac{( 2 + x ) ^{3} - 8}{x})

2 (s + 2)

\int - 3 cos (x) + 4 sec^{2} (x) d x

\frac{\partial}{\partial x} (4 cos (4 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=(1-ln(x))*integral of (-ln(x)-1)/((1-ln(x))^2)