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Tutorial Sheet 2 - Unit 1

This document contains 10 problems involving partial differential equations (PDEs). The problems involve finding complete integrals, solving PDEs, and determining characteristic equations for given PDEs. The PDEs contain mixed partial derivatives with respect to variables like x, y, z, and p, q which represent the first partial derivatives with respect to x and y.

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66 views1 page

Tutorial Sheet 2 - Unit 1

This document contains 10 problems involving partial differential equations (PDEs). The problems involve finding complete integrals, solving PDEs, and determining characteristic equations for given PDEs. The PDEs contain mixed partial derivatives with respect to variables like x, y, z, and p, q which represent the first partial derivatives with respect to x and y.

Uploaded by

td4520
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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SRM Institute of Science and Technology

Kattankulathur
DEPARTMENT OF MATHEMATICS
21MAB201T- TRANSFORMS AND
BOUNDARY VALUE PROBLEMS
UNIT - I Partial Differential Equations
Tutorial Sheet - 2
Sl. No. Questions Answer
Part - A
Find the singular integral of the PDE
1 4 z = y 2 − x2
z = px + qy + p 2 − q 2
x2 4 a 32
z = + ax − x
2 Find the complete integral of the PDE p+ q= x 2 3
+ ay + c

eay
3 Solve yp = 2 xy + log q z = x 2 + ax + +c
a

4 Find the complete integral of p + q = sin x + sin y z = ax − cos x − cos y − ay + c

 sin x sin y 
5 Solve p tan x + q tan y = tan z φ , =0
 sin y sin z 
Part - B

6 Solve (3 z − 4 y ) p + (4 x − 2 z )q = 2 y − 3x φ ( x 2 + y 2 + z 2 ,2 x + 3 y + 4 z ) = 0

x− y 
7 Solve ( x 2 − yz ) p + ( y 2 − zx )q = z 2 − xy φ , xy + yz + zx  = 0
 y−z 

8 Solve (2 z − y ) p + ( x + z )q + 2 x + y = 0 φ ( x2 + y 2 + z 2 , z + 2 y − x ) = 0

 x− y 
9 Solve ( y + z ) p + ( z + x)q = x + y φ , ( x + y + z )( x − y ) 2  = 0
 y−z 

1 1 1 
10 Solve x 2 ( y − z ) p + y 2 ( z − x)q = z 2 ( x − y ) φ  + + , xyz  = 0
x y z 

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