PSSOU MA/MSC (Mathematics) Previous Partial Differential Equation (L–293) Solved Assignment 2025

 (Assignment—1) 
Section—A 
1. Auxiliary equation of the linear partial differential equation P Q R p q   , are : 
(a) P, Q, R dx dy dz     
(b) 0 P Q R
 dx dy dz     
(c) P Q R
 dx dy dz    
(d) P Q R dx dy dz    
2. Partial differential equation formed by eliminating the arbitrary function f from 
2 2 ( ) z f x y   is : 
(a) 0 qy px    
  
(b) 0 xy pq    
(c) 0 yp xq    
(d) 2 2 z x y    
3. Classify the equation 2 2 2
 2 2 2 0 u u u
 x y z
      
   
 : 
(a) Parabolic 
(b) Elliptic 
(c) Hyperbolic 
(d) None of the above 
4. The steady state temperature distribution is governed by : 
(a) The Laplace’s equation 
(b) The Gauss’s equation 
(c) The Green’s equation 
(d) None of the above 
5. One dimensional wave equation is : 
(a) 
2 2 2
 2 2
 u u c
 t x
   
    
(b) 2 2
 2 2 2
 1 u u
 y c x
   
  
  
(c) 
2 2
 2 2 2
 1 u u
 t c x
   
    
(d) None of the above 
6. D’Alembert’s solution of the wave equation is : 
(a) ( , ) ( ) ( ) uxt x ct x ct      
(b) ( , ) ( ) ( ) uxt x ct x ct      
(c) ( , ) ( ) ( 2 ) uxt x ct x ct      
(d) None of the above 
 
  
7. 2 4
 0
 (2 3) t e t dt      
(a) 6e  
(b) 
6
 2
 e  
(c) 
6
 4
 e  
(d) 
6
 6
 e  
8. The solution of Dirichlet’s problem, if exists is : 
(a) unique 
(b) variable 
(c) infinity 
(d) None of the above 
Section—B 
9. Solve : 
2 2 p q x y    . 
10. Solve : 
25 40 16 0 r s t    . 
11. Solve : 
sin t xy  . 
12. Write the three-dimensional heat equation in spherical coordinates. 
13. Write one-dimensional wave equation. 
14. Write second mean value theorem.