NATIONAL OPEN UNIVERSITY OF NIGERIA
14/16 AHMADU BELLO WAY, VICTORIA ISLAND, LAGOS
SCHOOL OF SCIENCE AND TECHNOLOGY
MARCH/APRIL 2014 EXAMINATION
COURSE CODE: MTH 422
COURSE TITLE: PARTIAL DIFFERENTIAL EQUATION
TIME ALLOWED: 2Hrs. 30mins
INSTRUCTION: INSTRUCTION: ANSWER ANY FOURQUESTIONS.
INSTRUCTION: ANSWER ANY FOURQUESTIONS. 2Hrs. 30mins
1. Solve the vibration of an elastic string governed by the one dimensional wave equation.
subject to the boundary condition
14marks
2. Given
Find a. The initial element if 5marks
b. The characteristics stripe containing the initial elements 5marks
c.The integral surface which contain the initial element. 4marks
3. State and Prove CAUCHY KOVALEWASKI Theorem. 14marks
4a. Find the general solution of
,
By method of Lagrange multiplier 7marks
4b.. Derive the solution to the Cauchy problem
7marks
5. Prove that is the general solution of 14marks
6a) Determine the characteristic equation, the characteristic curve and the canonical form of
7marks
6 b) Prove that the equation in 6a above can be solved 7marks
7. By inspection, classify the following partial differential equations into the foolowing: non-linear,quasi-linearand linear. If linear, determine whether each is homogeneous or not
3.5marks each= 14marks
The total obtainable marks is 70 marks.
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Check anoda sample below
