To solve a homogeneous differential equation of the type
(
)
F
,
dy
x y
dx =
 =
y
g
x
⎛
⎞
⎜
⎟
⎝
⎠ (1)
We make the substitution
    y = v x (2)
Differentiating equation (2) with respect to x, we get
dy
dx  =
dv
v
+x dx