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

Explanation

` (dy)/(dx) = 1+ x+y+xy`
`dy/dx = (1+x) , +y(1+x) = (1+x)(1+y)`
` 1/(1+y) dy = (1 +x) dx`
Integrating we get, ` int 1/(1+y) dy = int (1+x) dx +c`
` log |1+y| = x+x^(2)/2 +c`
This is the general solution .