# KMA354 Partial Differential Equations Assignment 3. Due Thursday September 27, 2012

```KMA354
Partial Differential Equations
Assignment 3. Due Thursday September 27, 2012
1. Use the separation of variables technique to solve the following problem.
P DE :
∂2U
∂U
+ t (2 + 3x) =
2
∂x
∂t
BC1 :
U (0, t) = t2
t>0
BC2 :
U (1, t) = 1
t>0
IC1 :
U (x, 0) = x2
0<x<1
0 < x < 1, t > 0
(Try animating the solution with Mathematica or Matlab.)
2. Consider the equation
3x
d2 y
dy
+
−y =0 .
2
dx
dx
(i) Assess the singularity at x0 = 0.
(ii) Use Frobenius’ method at x0 = 0 to derive the independent solutions.
3. Use the Wronski determinant to show that the set of functions
xn
1,
(n = 1, 2, . . . , N )
n!
is linearly independent.
School of Mathematics & Physics
Assignment Cover Sheet
Student ID:
..........................................................
Name:
..........................................................
I declare that all material in this assignment is my own work except where there is clear acknowledgment
or reference to the work of others and I have read the University statement on Academic Misconduct
(Plagiarism) on the University website at www.utas.edu.au/plagiarism or in the Student Information
Handbook.
Signed ...................................................................... Date ..............................................
```