What is the solution for (1+ln(x)+y/x)dx=(5-ln(x))dy ?

The solution for (1+ln(x)+y/x)dx=(5-ln(x))dy is y=(xln(x))/(5-ln(x))+(c_{1})/(5-ln(x))

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(1+ln(x)+y/x)dx=(5-ln(x))dy

(1 + ln (x) + \frac{y}{x}) d x = (5 - ln (x)) d y

y = \frac{x ln ( x )}{5 - ln ( x )} + \frac{c _{1}}{5 - ln ( x )}

Solution steps

(1 + ln (x) + \frac{y}{x}) d x = (5 - ln (x)) d y

Solve linear ODE:

y = \frac{x ln ( x )}{5 - ln ( x )} + \frac{c _{1}}{5 - ln ( x )}

y = \frac{x ln ( x )}{5 - ln ( x )} + \frac{c _{1}}{5 - ln ( x )}

What is the solution for (1+ln(x)+y/x)dx=(5-ln(x))dy ?
The solution for (1+ln(x)+y/x)dx=(5-ln(x))dy is y=(xln(x))/(5-ln(x))+(c_{1})/(5-ln(x))