What is the solution for (1+ln(x)+y/x)dx=(7-ln(x))dy ?

The solution for (1+ln(x)+y/x)dx=(7-ln(x))dy is y=(xln(x))/(7-ln(x))+(c_{1})/(7-ln(x))

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(1+ln(x)+y/x)dx=(7-ln(x))dy

(1 + ln (x) + \frac{y}{x}) d x = (7 - ln (x)) d y

y = \frac{x ln ( x )}{7 - ln ( x )} + \frac{c _{1}}{7 - ln ( x )}

Solution steps

(1 + ln (x) + \frac{y}{x}) d x = (7 - ln (x)) d y

Solve linear ODE:

y = \frac{x ln ( x )}{7 - ln ( x )} + \frac{c _{1}}{7 - ln ( x )}

y = \frac{x ln ( x )}{7 - ln ( x )} + \frac{c _{1}}{7 - ln ( x )}

x \to - 7 lim (\frac{1}{x + 7})

[t]

\frac{d}{d x} (ln (e^{6 x}))

\int (\frac{1}{9 - x ^{2}}) d x

f^{^{''}} (x) = (7 + 6 x)^{e^{- 5 x}}

What is the solution for (1+ln(x)+y/x)dx=(7-ln(x))dy ?
The solution for (1+ln(x)+y/x)dx=(7-ln(x))dy is y=(xln(x))/(7-ln(x))+(c_{1})/(7-ln(x))