1
SRM Institute of Science and Technology
College of Engineering and Technology
Kattankulathur
Department of Mathematics
21MAB201T-Transforms and Boundary Value Problems
Tutorial Sheet-Unit-1
Q. No.
1.
Questions
PART-A (5 x 8 marks)
(i) Form the partial differenial
equation
by eliminating the arbitrary constants
a & b from z = x2 + a2 y 2 + b2 ,
(ii) Find a complete integral of x(1 + y)p = y(1 + x)q .
3.
Find the partial differenial equation by eliminating the arbitrary functions f and φ from
z = f (y) + φ (x + y + z).
Solve z = px + qy + p2 + q 2 .
4.
Solve x2 − yz p + y 2 − zx q = z 2 − xy .
5.
Solve (D + D0 )2 z = ex−y .
2.
1.
2.
3.
PART-B (3 x 15 marks)
(i) Form the partial differenial equation by eliminating the arbitrary function φ from
φ(x2 + y 2 + z 2 , z 2 − 2xy) = 0, and
(ii) Solve pq = k , where k is a constant.
0
0
Solve (D3 − 7DD 2 − 6D 3 )z = sin(x + 2y) + x3 .
(i) Solve x(y 2 − z 2 )p + y z 2 − x2 q = z(x2 − y 2 ).
(ii) Solve z 2 = 1 + p2 + q 2
Answers
4xyz = pq
z = a(logxy + x + y)
+b
r (1 + q) =
s (1 + p)
z = ax + by+
a2 + b2 (CS) 4z + x2 + y 2
= 0 (SS)
f (x + y + z ,
xyz) = 0
z = f1 (y + 2x)
+x f2 (y − x) +
x2 x−y
2 e
(p − q)z = y − x
z = ax + ka y + c
z = φ1 (y − x)+
φ2 (y − 2x)+
φ3 (y + 3x)+
1
x6
− 75
cox(x + 2y) + 120
f (x2 + y 2 + z 2
, xyz) = 0
cosh−1 z =
√ 1
(x + ay) + c
1+a2