Solve the following differential equation: `(dy)/(dx)=1-x+y-x y`

Explanation

`frac{d y}{d x}=1-x+y-x y`


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


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


Separate the variables


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


Integrating both sides


`int frac{d y}{1+y}=int(1 q-x) d x`


` log |1+y|=x-frac{x^{2}}{2}+k`