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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d}{d x} (7 - 4 e^{- x})

(- \frac{q ^{4}}{4} + \frac{2 q ^{3}}{3} + \frac{11 q ^{2}}{2} - 12 q)^{^{'}}

3 e^{6 x} \frac{d y}{d x} = - 36 \frac{x}{y ^{2}}

\int_{\frac{1}{5}}^{7} 6 x ln (5 x) d x

f (x) = (x^{2} - 9)^{2}

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