Reg No.:

Max. Marks: 100

A2100 Ras tg പി

سے

Name:

ന്റ്‌

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER B.TECH DEGREE EXAMINATION, JULY 2018
Course Code: MA102
Course Name: DIFFERENTIAL EQUATIONS

PART A>
Answer all questions, each carries 3 marks
Consider the initial value problem ‏برد ”بر‎ + 6xy= sinx, y(0)=3, )'(0) --1 .
Can this problem have unique solution in an interval containing zero? Explain.
Find any three independent solutions of the differential equation y”—y'=0.

Find the particular solution of the differential equation y’-6y'+9y=e™.

Using a suitable transformation, convert the differential equation

(2x-3) y"—(2x—3)y' +2y=(2x—3) into a linear differential equation with
constant coefficients.

State the conditions for which a function f(x) can be represented as a Fourier
series.

Discuss the convergence of a Fourier series of a periodic function f(x) of period
27.

Find the partial differential equation representing the family of spheres whose
centers lies on z-axis.

Find the particular solution of (D? -2DD' +2D’)z =sin(x—- y)

Write any three assumptions involved in the derivation of one dimensional wave
equation.

A string of length / fastened at both ends. The midpoint of the string is taken to a
height A and then released from rest in that position. Write the boundary
conditions and initial conditions of the string to find the displacement function
y(x,t) satisfying the one dimensional wave equation.

Write the fundamental postulates used in the derivation of one dimensional heat

equation.
1 7 ⋅ ⋅ ⋅∂∥≳∂⋮∥
Define steady state condition in one dimensional heat equation ar =a ae ⋅
PART B
Answer six questions,one full question from each module
Module 1

13 a) Discuss the existence and uniqueness of solution of the initial value problem

4
~ = -+= 0-3.

dx vx

b) Prove that 1 (४) = €` 4714 y,(x)= ச” form a fundamental system(basis) for the

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Duration: 3 Hours

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