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Question
Mathematics
If y(x) is solution of (x+1) (d y/d x)-x y=1, y(0)=-1, then y((-6/5)) is equal to
Q. If
y
(
x
)
is solution of
(
x
+
1
)
d
x
d
y
−
x
y
=
1
,
y
(
0
)
=
−
1
, then
y
(
5
−
6
)
is equal to
522
119
Differential Equations
Report Error
A
7
B
5
C
3
D
1
Solution:
We have
d
x
d
y
−
x
+
1
x
⋅
y
=
x
+
1
1
(linear differential equation) So, general solution is
y
(
x
+
1
)
e
−
x
=
∫
e
−
x
d
x
+
C
⇒
y
(
x
+
1
)
e
−
x
=
−
e
−
x
+
C
As
y
(
0
)
=
−
1
, gives
C
=
0
⇒
y
(
x
+
1
)
=
−
1
⇒
y
=
1
+
x
−
1
∴
y
(
5
−
6
)
=
5