Question

Solve dy/dx=xy+y/xy+x​

Answer 1

Step-by-step explanation:

We have,

$\frac{dy}{dx} = \frac{xy + y}{xy + x}$

$\implies(xy + x)dy = (xy + y)dx$

$\implies \: x(y + 1)dy = y(x + 1)dx$

$\implies \frac{(y + 1)}{y} dy = \frac{(x + 1)}{x} dx$

Integrating both sides ,

$\implies \int( 1 + \frac{1}{y} )dy = \int(1 + \frac{1}{x } )dx$

$\implies \: y + ln(y) = x + ln(x) + c$

$\implies(y - x) + ln( \frac{y}{x} ) = c$