(x+y)dy/dx = x^2+xy+x+1 ; y=v-x
So i did the substitution and ended up with vdv/dx - v =xv+x+1
and, if correct, i've no idea how to solve.
(x+y)dy/dx = x^2+xy+x+1 ; y=v-x
vdv/dx - v =xv+x+1
vdv/dx = v+xv+x+1
vdv/dx = v(1+x) + (1+x)
vdv/dx = (v+1)(1+x)
$\displaystyle \frac{vdv}{v+1} =(x+1)dx$
Integrate both sides
$\displaystyle \int{\frac{vdv}{v+1}} =\int{(x+1)dx}$
Integrate this thing and enjoy the sunny day