Question
Find a one parameter family of solutions of each of the following differential equation:
(x2 + x y) dy = (x2 + y2) dx
Solution
The given differential equation is
(x2 + x y) dy = (x2 + y2) dx
or
...(1)
Put y = v x so that

which is required solution.
(x2 + x y) dy = (x2 + y2) dx
or

Put y = v x so that


which is required solution.