10251
Reg. No.
SECOND SEMESTER B.TECH DEGREE EXAMINATION, JULY 2016
Course Code: MA-102
Course Name: DIFFERENTIAL EQUATIONS

Max. Marks: 100 Duration: 3 hrs

PART A
Answer all questions Each carries 3 marks

(1) Find the general solution of y” — y = 0

(2) Find the wronskian of the following e~* cos 5x ;e7* 5115 x

. d?y dy 2
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ನವು Solve न न + 4} ‏ح‎ ௪

2

Solve 22 + 2% = x2
(4) Solve ‏فيو‎ Sag ೫

(5) Express f(x) = x as aFourier series in the interval-17 7
(6) Obtain the half range Fourier sine series for the function e* 110 2

(7) Form the partial differential equation by eliminating the arbitrary function from

2 = y? + 2/ (‡ + 104 )
(8) Solve pvx + ೧/7 = 2

(9) Using the method of separation of variables solve a = 238 + 1८ where
u(x, 0) = 367%

(10) State the one dimensional wave equation with boundary conditions and
initial conditions for solving it

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Ox?
boundary and initial conditions for solving it

(12) Find the steady state temperature distribution in a rod of length 25cm, if the
ends of the rod are kept at 20°c and 70°c.

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⊂⊔⋟↧⊓⋔∁⊟∁∂∁⊖≺↴∐∂⊓∘⊓ 7 = what does «? indicate. State the

PART B
Answer one full question from each module
Module -1
(13) (9) Solve )''' — 8y” + 37 y’—50 y=0 (6)