F
dy +C
∫
Example 19 Find the general solution of the differential equation 
cos
dy
y
x
dx −
= Solution Given differential equation is of the form
P
Q
dy
y
dx +
=
, where P = –1 and Q  =  cos x
Therefore
I F =
1 dx
x
e
e
  
 
Multiplying both sides of equation by I F, we get
x
x
dy
e
e
y
dx
−
−−
 = e–x cos x
or
(
dy yex)
dx
−
= e–x cos x
On integrating both sides with respect to x, we get
ye– x =
cos
C
ex
x dx
−
+
∫