A

(0) Find the general solution of the equation x*y" + xy’ + (x? — 0.25)y = 0

_ ८05८

tne
OR
14. (a) Find a second order homogeneous linear ODE for which x, xlogx are

solutions and solve the IVP with y(1) = 2, y (1) = 4.

(b) Solve the IVP y"— 4y'+ 99 = 0, y(0) = 0,y (0) = -8

Module- 1
15. (a) Solve (D? - 2D + 5)y = e?*sin x
(b) Solve ((x + 1)2 4 + ( + 1) = ௦48௫௩௮
OR

८० ‏و‎ − 1
+ 2x? 4 + 2y = 10 (८ +5)

16. (a) Solve x? aa

iv 8 2.
(b)Solve y - 49 +5y = ‏کت‎ by method of variation of parameters

Module - 1
17. (a)Find the Fourier series representation of f(x) = x sinx periodic with
period 27, defined in0(b)Find the Fourier cosine series of f(x) = ೦೦5%, 0 > × < 1/2
OR

18. (a)Find the Fourier series expansion of f(x) = e~* in-c
(b)Develop the Sine series representation of f(x) = ۶ ட்‌ 7 9 து ಸ = 1

Module - IV
19. (a) Solve (y + 2x)p - (x + 92) ६ =x? -- #2
(b)Find the differential equation of all spheres of fixed radius having their
centres in XY —plane.
OR
20. (a)Solve (03 -200'- 150%) 25120

2