A

Reg. No. Name:

B2A102

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER B.TECH DEGREE EXAMINATION, MAY 2017

MA 102: DIFFERENTIAL EQUATIONS

Max. Marks: 100 Duration: 3Hours

15.

PART A
Answer all questions. 3 marks each.

. Solve the initial value problem + - ‏ہر‎ = 0, y(0) = 4, ै (0) = -2

Show that ९2, e3*are linearly independent solutions of the differential equation

2
= − a +6y=0 1 - % > x > +0,What is its general solution?

Solve ५ acy +5 = -2y =0

Find the particular integral of (D? + 4D + 1)y = e*sin3x

Find the Fourier series 07100-0, ‏7ح‎
Obtain the half range cosine series of f(x)= x7,0 ८

Form the partial differential equation from z = xg(y) + yf (x)

Solve (+ - ‏مزج‎ + (x-y)q = (2-2)

Write down the important assumption when derive one dimensional wave equation.

Solve ३४८५ +2uy=0 with u(x,0)=4e~* by the method of separation of variables.

, Solve one dimensional heat equation when k> 0

. Write down the possible solutions of one dimensional heat equation.

PART B
Answer six questions, one full question from each module.

Module I

. a) Solve the initial value problem ‏اہر‎ - 4y1 + 139 = 0 with y(0)=-1 ,y1(0) = 2

(6)
b) Solve the boundary value problemy” - 10y! + 25) = 0 , y(0)=1,y(1)=0 (5)
OR

.a) Show that y,(x) = e7** and y2(x) = xe7** are solutions of the differential

equation <> + 84 + 16) = 0 . Are they linearly independent? (6)
b) Find the general solution of (D* + 3D? - 4)y = 0. (5)

Module 11
a) Solve (D3 + 8 ‏ہرز‎ = sinx cosx + 672 (6)

0) Solve y!! + y = tan x by the method of variation of parameters. (5)
OR

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