MTH422 : Partial Differential Equations (2018)

NATIONAL OPEN UNIVERSITY OF NIGERIAN

Plot 91, Cadastral Zone, NnamdiAzikiwe Express Way, Jabi-Abuja

FACULTY OF SCIENCES

January\February Examination 2018

 
Course Code: MTH422
Course Title: Partial Differential Equations
Credit Unit: 3
Time Allowed: 3 Hours
Total Marks: 70%
 
INSTRUCTION: ANSWER QUESTION ONE(1) AND  ANY FOUR (4)
QUESTIONS (TOTAL = 5 QUESTIONS IN ALL)
 
 
1(a) Find the general solution of
.8 marks
Hence solve
5 marks
1(b)Which of the following P.D.E is linear, quasi – linear or non- linear. If the P.D.E is linear, state whether it is homogeneous equation or not
i.                    1 marks
ii.                  1 mark
iii.                                                                        1 mark
iv.                                                                               1 mark
1(c) solve the partial differential equation by the method of characteristics
5 marks
2(a) State the condition under which the equation:  would be;
i.                    Hyperbolic                                                                                            2 marks
ii.                  Elliptic                                                                                                  2 marks
iii.                Parabolic                                                                                              2 marks
2(b)Find the first partial derivatives of                                        6 marks
3(a).   Find the general solution of
,
By the method of Lagrange multiplier                                      6marks
3(b)  Derive the solution to the Cauchy problem
6marks
4.Solve the vibration of an elastic string governed by the one-dimensional wave equation
, where u(x, y) is the deflection of the string
12 marks
5(a) Find the first partial derivatives of 6 marks
5(b) Find the general solution of the following:
6 marks
subject to
6        Explain the terms:
i.                    Partial differential equation                                                                  2 marks
ii.                  Order of differential equation                                                               2 marks
iii.                Quasi – linear equation                                                                       2 marks
iv.                General solution of P.D.E                                                                  2 marks
v.                  Non-linear P.D.E                                                                                2 marks
vi.                Ordinary Differential equation                                   2marks
You can get the soft copy for this course or the exam summary answers for this course from 08039407882

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