01000MA102032103 Pages: 3

Reg No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
B.Tech Degree 51,52 (S,FE) Examination May 2021 (2015 Scheme)

Course Code: MA102
Course Name: DIFFERENTIAL EQUATIONS
Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all Questions. Each question carries 3 Marks Marks

1 Solve the ODE, y’” +y = 0 (3)
2 Show that € ॐ and 02" are linearly independent solutions of y"— 5y'+6y (3)

0
3 Solve,(D? + 3D + 2)y = 5 (3)
4 Using a suitable transformation, convert the differential equation (3)

(1 + 2८) ‏"بك‎ + (1 + x)y’ = (2x + 3)(2x + 4) into a linear differential equation

with constant coefficients
5 Represent the function f(x) = x? as a Fourier series in the interval(—z, 7) (3)
6 Find the half range Fourier sine series of f(x) = e* 10 < ८ < 1 (3)
7 Form a PDE by eliminating the arbitrary function from z = y? + 2f ८ +logy) (3)
8 Find the P.I. of (02 - 5DD' + 4D’")z = sin(4x + 9) (3)
9 Solve xo − 20 = 0 using method of separation of variables. (3)
10 A tightly stretched flexible string has its ends at x =Oand x = | At time (3)

1-0,

the string is given a shape defined by f(x) = ux(l— x), where ‏غز‎ is a constant,

and then released. Write the boundary and initial conditions
11 Write down the possible solutions of one dimensional heat equation. (3)

12 The ends A and B of a rod of length 1 have the temperature ൪0 and 9१८ (3)
respectively until steady state conditions prevail. Find the initial temperature

distribution of the rod.

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