Part-A
1
Find P.I of
'' 2 ' sinh2y y y x+ + =
.
2
Find the P.I for
( )
22x
D D y e−=
3
Transform the equation
3 2 2
( 3 5 ) 2x D x D x y+ + =
into the linear equation with
constant coefficient.
4
Solve:
022
2
2
=−+ y
dx
dy
dx
yd
5
Solve:
( )
24 4 0D D y+ + =
6
Form the PDE by eliminating the arbitrary constants a and b
from(x+a)2+(y+b)2+z2=1.
7
Form the PDE by eliminating the arbitrary constants from z=(x+a)2(y-b)2.
8
Eliminate the function ‘f’ from z=f(x2- y2).
9
Form the PDE by eliminating the arbitrary function from ф(z2-xy,x/z)=0
10
Find Complete integral of z = px +qy + pq
Part-B
1
Solve (D2-4D+4)y= cos4x.
2
Solve (D2+1)y= sinxsin2x.
3
Solve
xy
dx
yd 2tan44
2
2
=+
by using method of variation of
parameters.
4
Solve
xy
dx
yd sec
2
2=+
, using methods of variation
of parameters.
5
Solve
( ) ( )
2
2
2 2 3 4
2
d y dy
x x y x
dx
dx
+ − + + = +
6
Solve
xy
dx
dy
x
dx
yd
x612)32(2)32( 2
2
2=−+−+
7
Solve:(x2- y2- z2)p+2xyq=2xz
8
Solve
).
22
()
22
()
22
(yxzqxzypzyx −=−+−
9
Find the singular integral of 𝑧 = 𝑝𝑥 +𝑞𝑦 + 𝑝2+𝑝𝑞 + 𝑞2
10
Find singular integral of PDE z = px +qy +
22
1qp ++