Reg No.: Name:

Max. Marks: 100

“1101

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER B.TECH DEGREE EXAMINATION (R & S), MAY 2019

Course Code: MA102
Course Name: DIFFERENTIAL EQUATIONS:

PART A
Answer all questions, each carries 3 marks

Find the general solution of <2 73 = 0

Find the Wronskian of e* cos 2x and e* sin 2x

Find the Particular Integral of ‏اکر‎ - 4" 5y = 4 cos2x.

Find the particular integral of ‏يرك + 4 + نے‎ = sinh 2x

Evaluate the coefficient ൨... in the Fourier series expansion for f(x) = {sin x] in
எவ வர

Find the half range Fourier sine series representation of f(x) = k in (0,77)

Find the partial differential equation of all spheres having their centre lies on z-

axis.

ക.

Form the partial differentia! equation of 2 = ~) by eliminating the arbitrary
function f.

au au -3+ , 5 ⋅ ∙
Solve >= ‏ماپ‎ (0,y) = ‏وع‎ >, using the method of separation of variables.
A tightly stretched string of length / is fixed at both ends and pulled from its mid
point to a height h and realised from rest from this position. Write down the
initial and boundary conditions.
Find the steady state temperature distribution in a rod of length 30 cm, if the ends
of the rod are kept at 20°C and 80°¢

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

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Duration: 3 Hours