A

(b)Determine all possible solutions to the initial value problem
‏ار‎ =1+y?,y(0) = 0 in [| < 3, |) > 2 (5)

OR

(4) न the general solution of 9? ‏“نير‎ - 9 y”—11 y’-4 y=0 (6)
(b)Determine all possible solutions to the initial value problem

+ = y2,y(0) = 0. இது

Module - IT
(15) (a)Solve by method of variation of parameters +y = xsinx (6)

(b)Solve i = +y =xe*sinx. (5)
OR
(16) (6806 पी ಸಖಿ _ 4) =x? + 2108 %. (6)
(b)Solve = − 3 + 39 = sin3xsin2x. (5)
Module - 111

(17) (a)Obtain the Fourier series for the function f(x) given by
f@)=

2.
1+—-n
(6)
1-2 o7
(b)Obtain the Fourier series to represent the function
f(x) =|sinx|; - < ‏ع‎ > 7 (5)
OR
(18) (a)Expand the function f(x) = x sinx 35 Fourier series in the interval
<> (6)

(b)Find the half range cosine series for the function f(x) = x? in the range
03% 37 (5)