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Reg. No. > ` ` Name: 4
SECOND SEMESTER B.TECH. DEGREE EXAMINATION, MAY/JUNE 2016
MA 102 : DIFFERENTIAL EQUATIONS
Max. Marks : 100 । Duration : 3 Hours

۲۵۸۲۳۲۲ - ۸

Answer all questions 8೧66800 question carries 3 marks. `

1. Determine a linearly independent solution of the differential equation
(x2 + 1) #॥ - 2xy! + 2y = 0 if ‏رلا‎ = x is solution.

2. Solve the differential equation ٢۷ + 6\/॥॥ + 9\/॥ = 0.

‘8, Find the particular integral of the differential equation (02 — 2D + 1)y = xe*.

4, Solve by the method of variation parameters, (02 + 4(۷ = tan 2x.

इ. Develop the Fourier series of f (x) = x? in-26. Find the Fourier sine series of f (x) = e*in0
7. Obtain the partial differential equation by eliminating f and g from z = xf (y) + yg (x).
8. Solve the partial differential equation (y? + 22 - xyq + xz=0.

9. 0 the solution of the wave equation 20 = ‏نہ‎ using method of separation

ox“ റ്‌ ٢
of variables when the separation constant k < 0.

10. Write any two assumptions involved in deriving one dimensional wave equation.

11. Find the steady state temperature distribution in a rod of length 20 cm if the ends
of the rod are kept at 10° C and 70° C.
du 90 .. 5
12. Solve त्र = பூர subject to the conditions ‏نا‎ (0, ॥ = ५ (1, 0 = 0 01 > 0 200
‏نا‎ (4,0) = 3sin nm ,0 < <> 1. (123 = 36 Marks)

P.T,O.