What is the solution for (1+ln(x)+y/x)dx=(8-ln(x))dy ?

The solution for (1+ln(x)+y/x)dx=(8-ln(x))dy is y=(xln(x))/(8-ln(x))+(c_{1})/(8-ln(x))

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(1+ln(x)+y/x)dx=(8-ln(x))dy

(1 + ln (x) + \frac{y}{x}) d x = (8 - ln (x)) d y

y = \frac{x ln ( x )}{8 - ln ( x )} + \frac{c _{1}}{8 - ln ( x )}

Solution steps

(1 + ln (x) + \frac{y}{x}) d x = (8 - ln (x)) d y

Solve linear ODE:

y = \frac{x ln ( x )}{8 - ln ( x )} + \frac{c _{1}}{8 - ln ( x )}

y = \frac{x ln ( x )}{8 - ln ( x )} + \frac{c _{1}}{8 - ln ( x )}

\frac{d}{d x} (ln (sinh (2 x)))

\int \frac{e ^{x}}{1 + 9 e ^{2 x}} d x

x \to 3 lim (2 e^{x - 3})

\frac{s}{( s - 1 ) ^{2} + 4}

\frac{d}{d x} (5^{x} + 7^{x})

What is the solution for (1+ln(x)+y/x)dx=(8-ln(x))dy ?
The solution for (1+ln(x)+y/x)dx=(8-ln(x))dy is y=(xln(x))/(8-ln(x))+(c_{1})/(8-ln(x))