Question

Find the general solution of differential equation:

dy/dx = 1 + x + y + xy

Answer 1

It is given that

Answer 2

\(\frac{dy}{dx} = 1 + x + y + xy\)

\(\frac{dy}{dx} = (1 + x) + y(1 + x)\)

\(\frac{dy}{dx} = (1 + x) +(1+y)\)

\(\frac{dy}{(1 +y)} = (1 + x) dx\)

\(\int \frac{dy}{(1 + y)}= \int (1 + x)dx\)

\(\log_e |1 + y|= x + \frac{x^2}2 + c\)