(1)
Let
F(x, y) =
2
x
y
x
 y
 
Now
F(λx, λy) =
0
(
2 )
( , )
(
)
x
y
F x y
x
y
 
  
 
 
 
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MATHEMATICS
400
Therefore, F(x, y) is a homogenous function of degree zero So, the given differential
equation is a homogenous differential equation Alternatively,
2
1
1
y
dy
yx
dx
x
⎛
⎞
⎜+
⎟
= ⎜
⎟
⎜
⎟
−
⎝
⎠
 =
y
g
x
⎛
⎞
⎜
⎟
⎝
⎠ (2)
R