10252
Reg. No.

Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

SECOND SEMESTER B.TECH DEGREE SPECIAL EXAMINATION, AUGUST 2016

Course Code: MA-102
Course Name: DIFFERENTIAL EQUATIONS

Max. Marks: 100 Duration: 3 hrs
PART A
Answer all questions Each carries 3 marks
1. Find ordinary differential equation for the basis ९-*४2, அதது
Reduce y"= 9 ' to 1* order differential equation and solve.

+ ~ YN

Find the particular solution 10 (D* - 714) y = sin mx

Use variation of parameters to solve y" + y = secx

Find the Fourier coefficient ஐ, for the function f(x) = 1 + |x| defined in
-3> >> 3

Develop the Fourier Sine series of f(x) =x 11 0 > ‏عد‎ > 7

Obtain the partial differential equation by eliminating arbitrary function from
x? + 9 + 22 = f(xy)

Solve y?zp + ‏وج ةبر‎ = xy?

Solve ८८ + uy = 0 using method of separation of variables

. A finite string of length L is fixed at both ends and is released from rest with a

displacement f (x). What are the initial and boundary conditions involved in

this problem?

. Write all the possible solutions of one-dimensional heat transfer equation

12.

Find the steady state temperature distribution in a rod of length 30cm having
the ends at 20° C and 80° C respectively.
PART 8

Answer one full question from each module
Module -I

. (a) Verify linear independence of e~*cosx and e~*sinx using Wronskian and

hence solve the initial value problem )' + 2y + 29 = 0, ೫(೦) = 0, y (0) =
15