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
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