Therefore,
I F =
2
2
x
x dx
e
e
−
−∫
=
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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 Therefore,       I =
2
2
–
x
t
t
e dt
e
e
−
−
= −
=
∫
Substituting the value of I in equation (2), we get
2
2
x
y e
−
 =
2
2 + C
 
 
x
e
or
y =
2
2
1
C
x
e
− +