Solve the following differential equations: `(dy)/(dx)=1+x+y+x y` (ii) `y-x(dy)/(dx)=a(y^2+(dy)/(dx))`

Answer

`y/(1-ay)=c(a+y)`

Explanation

`y-x(dy)/(dx)=a(y^(2)+(dy)/(dx))`
or `int(dx)/(a+x)=int(dy)/(y-ay^(2))=int(1/y+a/(1-ay))dy` [By partial fractions]
Integrating we get
`log(a+x)+logc=logy-log(1-ay)`
Which is arbitary positive constant.
Thus, the solution can be written as `y/(1-ay)=c(a+x)`