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 423
COURSE TITLE: INTEGRAL EQUATION
TIME ALLOWED: 3HOURS
INSTRUCTION: COMPLETE ANSWERS TO ANY FIVE (5) QUESTIONS BEAR FULL MARKS
1(a) With proper integration and differentiation, convert the understated differential equation into integral equation.
y”(x) + a1(x) + a2(x)y(x) = f(x) with the initial condition y(0) = 0; y(0) = y1-7marks
1(a) Using appropriate method, form the integral equation corresponding to
Y” + 2xy’ + y = 0, y(0) = 1, y’(0) = 0. — 7marks
2(a) Solve the integral equation
-5marks
2(b) Solve the integral equation -9marks
3 Find the eigen values and eigen function of the system -14marks
4(a) Find an integral formulation for the problem defined by
+ 4y = f(x), , y = 0 at x = 0 and y = 0 at x = -7marks
4(b) Transform the problem defined through + λy = 0 when y = 0 at x = 0 and
y’ = 0 at x = 1 into integral equation form. -7marks
5. Solve the integral equation -14marks
6(a) Solve the integral equation -7marks
6(b) Solve the integral equation 3sinx + 2cosx = – 7marks
7 Let be an orthogonal system, and let be continuous.
Set .Show that and are known as the Fourier’s coefficient. -14marks
You can get the exam summary answers for this course from 08039407882
Check anoda sample below
