Question

find the particular intrigal
(D²-1 ) y=
$x{2} + x$
​

Answer 1

y
p
=
1
D
2
+
1
x
cos
⁡
x

=12+1..
=
1
D
2
+
1
R
.
P
.
o
f
x
e
i
x

=R.P. of 1(+)2+1
e
i
x
1
(
D
+
i
)
2
+
1
x

=R.P. of 12+2
e
i
x
1
D
2
+
2
D
i
x

=R.P. of 12(1+2)
e
i
x
1
2
D
i
(
1
+
D
2
i
)
x

=R.P. of (1+2)−12
e
i
x
(
1
+
D
2
i
)
−
1
2
D
i
x

=R.P. of (1−2+….)2
e
i
x
(
1
−
D
2
i
+
…
.
)
2
D
i
x

=R.P. of 12(+2)
e
i
x
1
2
D
i
(
x
+
i
2
)

=R.P. of (2+4)
e
i
x
(
x
2
+
i
x
4
i
)

=2sin+cos4