Question
Show that the following differential equation is homogeneous and find a primitive of it. Derive the solution wherever possible:
(x2 + y2) y' = 8 x2 - 3 x y + 2 y2
Solution
The given differential equation is
Put
Separating the variables, we get,
Integrating,
Put
...(1)
Put
(1) can be written as
...(2)
Equating coefficients in (2) of
V2) 1 =A - B
v) 0 = 2 B - C
which is required primitive.
Put
Separating the variables, we get,
Integrating,
Put
...(1)Put
(1) can be written as
...(2)Equating coefficients in (2) of
V2) 1 =A - B
v) 0 = 2 B - C
which is required primitive.
