(2)
Differentiating equation (2) with respect to x, we get
dy
dx  =
dv
v
+x dx (3)
Substituting the value of dy
dx  from equation (3) in equation (1), we get
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DIFFERENTIAL EQUATIONS
399
dv
v
+x dx
 = g (v)
or
dv
x dx  = g (v) – v (4)
Separating the variables in equation (4), we get
( )
dv
g v
−v
 = dx
x (5)
Integrating both sides of equation (5), we get
( )
dv
g v
−v
∫
 =
1
C
xdx
+
∫