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

Question

Solve the following differential equation:

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

Answer 1

Given differential equation xy\(\frac{\text{dy}}{\text{dx}}\) = 1 + x + y + xy

Find: Find the general solution of this differential equation.

= y – log|y + 1| = log|x| + x + log|C|

= y = log|x| + x + log|y + 1| + log|C|

Hence, y = log|cx(y + 1)| + x