(1)
This is a linear differential equation of the type 
P
Q
dy
dx +y
=
, where P = – x and Q = x Therefore,
I F =
2
2
x
x dx
e
e
−
−∫
=
© NCERT
not to be republished
DIFFERENTIAL EQUATIONS
413
Hence, the solution of equation is given by
2
2
x
y e
⋅−
 =
(
)
2
2
( )
C
x
x
dx
e
−
+
∫ (2)
Let
I =
2
2
( )
x
x
dx
e
−
∫
Let 
2
x2
t
−
= , then – x dx = dt or x dx = – dt