Solve the given Differential Equation Solve the non-linear first order differential equation
$$\frac{dy}{dx}=\frac{x+2y-5}{2x+xy-4} $$
I tried substituting $x=X+h$ and $y=Y+k$ but the $xy$ term is creating problem. 
How to solve it?
Any suggestion is appreciated.

$\dfrac{dy}{dx}=\dfrac{x+2y-5}{2x+xy-4}$
$(x+2y-5)\dfrac{dx}{dy}=(y+2)x-4$
This belongs to an Abel equation of the second kind.
Let $u=x+2y-5$ ,
Then $x=u-2y+5$
$\dfrac{dx}{dy}=\dfrac{du}{dy}-2$
$\therefore u\left(\dfrac{du}{dy}-2\right)=(y+2)(u-2y+5)-4$
$u\dfrac{du}{dy}-2u=(y+2)u-2y^2+y+6$
$u\dfrac{du}{dy}=(y+4)u-2y^2+y+6$
Let $s=y+4$ ,
Then $\dfrac{du}{dy}=\dfrac{du}{ds}\dfrac{ds}{dy}=\dfrac{du}{ds}$
$\therefore u\dfrac{du}{ds}=su-2(s-4)^2+s-4+6$
$u\dfrac{du}{ds}=su-2s^2+17s-30$
Let $t=\dfrac{s^2}{2}$ ,
Then $s=\pm\sqrt{2t}$
$\dfrac{du}{ds}=\dfrac{du}{dt}\dfrac{dt}{ds}=s\dfrac{du}{dt}$
$\therefore su\dfrac{du}{dt}=su-2s^2+17s-30$
$u\dfrac{du}{dt}=u-2s+17-\dfrac{30}{s}$
$u\dfrac{du}{dt}-u=\mp2\sqrt{2t}+17\mp\dfrac{30}{\sqrt{2t}}$
This belongs to an Abel equation of the second kind in the canonical form.
Please follow the method in https://arxiv.org/ftp/arxiv/papers/1503/1503.05929.pdf or in http://www.iaeng.org/IJAM/issues_v43/issue_3/IJAM_43_3_01.pdf
