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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

SECOND SEMESTER B.TECH DEGREE EXAMINATION, DECEMBER 2018

Max. Marks: 100

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13 a)
b)

Course Code: MA102
Course Name: DIFFERENTIAL EQUATIONS

PART A
Answer all questions, each carries 3 marks

Find a general solution of the ordinary differential equation y” + y = 0

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

Find the particular integral of the differential equation 2“ + y = cosh5x

Using a suitable transformation, convert the differential equation.

(3x + 2)?y" + 5(3x+2)y'-3y =x? + ‏+ع‎ 1 into a linear differential
equation with constant coefficients.

If f(x) is a periodic function of period 2L defined in [—L, 1]. Write down Euler’s
Formulas ‏روت‎ ay, ‏برط‎ for f (x).

Find the Fourier cosine series of f(x) = x? in 0
Find the partial differential equation of all spheres of fixed radius having their
centres in xy-plane.

Write any three assumptions involved in the derivation of one dimensional wave

equation.

a ⋅ ⋅ ⋅
Solve x = - 2 ‏آ9‎ = 0 using method of separation of variables.

Find the steady state temperature distribution in a rod of 30 cm having its ends at
20°C and 80°C respectively,

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

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

Module 1
Solve the initial value problem +" + 4y' + 5) = 0, y(0) = 2,)'(0) = -5,

Find a basis of solutions of the ODE (x* —x)y” —xy’+y=0, if y= x is a

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