What is the solution for (1+ln(x)+y/x)dx=(6-ln(x))dy ?

The solution for (1+ln(x)+y/x)dx=(6-ln(x))dy is y=(xln(x))/(6-ln(x))+(c_{1})/(6-ln(x))

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(1+ln(x)+y/x)dx=(6-ln(x))dy

(1 + ln (x) + \frac{y}{x}) d x = (6 - ln (x)) d y

y = \frac{x ln ( x )}{6 - ln ( x )} + \frac{c _{1}}{6 - ln ( x )}

Solution steps

(1 + ln (x) + \frac{y}{x}) d x = (6 - ln (x)) d y

Solve linear ODE:

y = \frac{x ln ( x )}{6 - ln ( x )} + \frac{c _{1}}{6 - ln ( x )}

y = \frac{x ln ( x )}{6 - ln ( x )} + \frac{c _{1}}{6 - ln ( x )}

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

\frac{\partial}{\partial x} (4 x e^{x})

\int_{0}^{\infty} x e^{- a x} d x

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

\frac{d}{d x} ((x^{2} + 17) (x^{3} - 3 x + 1))

What is the solution for (1+ln(x)+y/x)dx=(6-ln(x))dy ?
The solution for (1+ln(x)+y/x)dx=(6-ln(x))dy is y=(xln(x))/(6-ln(x))+(c_{1})/(6-ln(x))