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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER B.TECH DEGREE EXAMINATION(S), DECEMBER 2019
Course Code: MA102
Course Name: DIFFERENTIAL EQUATIONS

Max. Marks: 100 Duration: 3 Hours
PART A
Answer all questions, each carries 3 marks

1 Find a general solution of the ordinary differential equation ೫ '” + y = 0 (3)
2 Reduce to first order and solve. yy” = 30൮7). (3)
3 Find the particular integral of y" — 4y'— Sy = 4 cos2x. (3)
4 Using a suitable transformation, convert the differential equation
(८२ ° + xD + 1)y = logx into ೩ linear differential equation with (3)
constant coefficients.
5 If f(x) is a periodic function of period 25 defined in [—z, 7]. Write down Euler’s
Formulas മം. நே b, for f(x). (3)
6 Find the half range Fourier cosine series of the function f(x) =x in the range
O7 Find the PDE by eliminating arbitrary function © from xyz = g(x +y + 2). (3)
8 Solve (2 + 2D'}(D — 3D'}*z = 0. (3)
9 Write any three assumptions involved in the derivation of one dimensional wave
Equation. (3)
10 A tightly stretched string of length / is fixed at both ends and pulled from its mid

point to a height h and released from rest from this position. Write down the (3)

initial and boundary conditions.

1] Write all possible solutions of one dimensional heat equation. (3)
12 Find the steady state temperature distribution in a rod of length 7 the ends are
3
kept at 032 and 100°C. (3)
PART B
Answer six questions,one full question from each module
Module 1
13 9) Solve ऊ“ - 2y’+ y = 0, ೫(0) = 1, y'(0) = 2. (6)

b) Find a basis of solutions of the ODE (६ —x)y" - ഹ + ऊ = 0, if $= > isa (5)

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