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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER B.TECH DEGREE EXAMINATION, DECEMBER 2018
ಷಃ Course Code: MA102
Course Name: DIFFERENTIAL EQUATIONS

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all questions, each carries 3 marks

1 Find a general solution of the ordinary differential equation y” + y = 0 (3)
2 Find the Wronskian of e* cos 2x and e* sin 2x (3)
3 Find the particular integral of the differential equation y” + y = cosh5x (3)
4 Using a suitable transformation, convert the differential equation.

(3x + 2)?y" + 5)3 +2)y'-3y=x?+x+1 into a linear differential (3)

equation with constant coefficients.

5 If f(x) is a periodic function of period 2L defined in [—L, L]. Write down Euler’s 7
Formulas 00, ஷே by for f (x).
6 Find the Fourier cosine series of f(x) = x” in 07 Find the partial differential equation of all spheres of fixed radius having their 7
centres in xy-plane.
8 Find the particular integral of r+ ‏۔ و‎ 2t=/2x + y. (3)
9 Write any three assumptions involved in the derivation of one dimensional wave (3)
equation.
10 Solve ८०४ − മും ട 0 using method of separation of variables. (3)
1] Find the steady state temperature distribution in a rod of 30 cm having its ends at
20°C and 80°C respectively. ©)
12 Write down the possible solutions of the one dimensional heat equation. (3)
PART B
Answer six questions, one full question from each module
Module 1
13 a) Solve the initial value problem y” + 4)' + 59 = 0, y(0) = 2,y'(0) = -5, (5)

ட) Find a basis of solutions of the ODE (४८ -x)y"” —xy'’+y=0, if ¢= + isa (6)

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