A B2A0104

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

Course Code: MA102 Course Name: DIFFERENTIAL EQUATIONS

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all questions. Each carries3 marks.
1 Find a second order homogeneous linear ODE for which ൦ and 6 are the (3)
solutions.
2 Find a basis of solutions of y!!—y'=0. (3)
3 Find the particular integral of (D?—4)y=x?. (3)
4 Solve ( 02 + 3D + 2 jy 5. (3)
5 Expand ‏عم‎ — x? ina half range sine series in the interval ) 0 , ಸ). (3)
6 Expand f(x) in Fourier series in the interval ( -2 , 2) when (3)
1) = {0 -21 0 > > 2
7 Obtain the partial differential equation by eliminating the arbitrary function from
(3)z=f( x+y’).
8 Solve xp + yq = 32. (3)
Using the method of separation of variables solve uy -u=0. (3)
10 Write down the possible solutions of one dimensional wave equation. (3)
11 Find the solution of one dimensional heat equation in steady state condition. (3)
12 State one dimensional heat equation with boundary conditions and initial (3) conditions
for solving it.
PART ‏ا‎
‎Answer six questions,one full question from each module.
Module 1
13 a) Reduce to first order and solve x*y!! — 5xy! + ‏رو‎ = 0.Given ४1 = x’ is a solution. (6)
b) Solve the initial value problem 4y!! — 25y = 0 where y(0) = 0 , y'(0) = -5. (5) OR

14 a) Show that the functions e*Cosx and ടമാ are linearly independent. Form a (6) second
order linear ODE having these functions as solutions.

b) Solve ‏۷اپ‎ — 29111 + 5y!!— 8y! + 4y =0. (5)
Module 1
15 a) Solve x3d—sy3 + 2x2 _ 4292 + 2) = 10 (x +1). (6)
dx dx x
b) Solve y!! _ 41 + 3y =e*Cos 2x. (5)
OR
16 a) Solve y'! + y = Cosec x using the method of variation of parameters. (6) b) Solve

(D?—2D + 1 )y=xSinx. (5)

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