The suitable form of the particular solution for the DE y" +3y+2y=e (2+1) sin 2t+3e cost + 4e' is a) Y(t)=(At²+Bt+C) e' sin 2t+(Dt² + Et +F) e cos 2t+(G cost+H sint)e + le b) Y(t)=(At² + Bt) é sin 2t+(Dt² + Et) e* cos 2t+(G cost+H sint) e* c) Y(t)=(At² + Bt+C)e' sin 2t+ (Dt² + Et + F) e cos2t+(Gt+H)e* cost+Ie' d) Y(t)=(At+B)e' sin 2t+ (Ct+D) e' cos 2t+(Ecost+Fsint)e +Ge The principle value of (1+i) is π i a) (1+i) exp +-log 2 42 πί b) (1+i)exp -log 2 42 π c) (1-1) exp +-log 2 42 d) (1+1)explog 2 The Fourier Cosine series of the function f(x)=3-x, 0<x<3 is 3 a) f(x): 6 = + Σ 2 π n=1 1- cos(nл) n² ηπ COS x 3 8 32 + 6 Π b) f(x) =Σ n=1 3 c) ƒ (x) = 3/25 d) ƒ (x) = + 1- cos(n) n² (1-cos(nл) ηπ COS ·x 3 IM Σ ηπ COS -x n² 3 મગ IM Σ 1-cos (n) ηπ COS X n' 3 The solution to the heat conduction problem u4u, 0<x<2, t>0 u(0,t) =0, u(2,t) = 0, t>0 u(x, 0) = 2 sin Π.Χ 2 - sin x + 4 sin 2лx, 0≤x≤2 is a) u(x,t)=sin TTX e 2 b) u(x,t) = 2sin(x) e - sin(x)e +4 sin(2x)e¯* - - sin(xx)e¯½³. +4 sin (2x)e¯* π.Χ c) u(x,t) = 2 sin -sin(xx) e +4 sin(2x)e¯* 2 d) u(x,t) = 2 sin ( TTX e 2 16 - sin(x)e + 4 sin (2x) e¯* The pole of the function 3z2+1 z³ (z² + 2iz+1) a) z=-2 with multiplicity 6 b) z=-2 with multiplicity 3 c) z=2 with multiplicity 2 d) z=2 with multiplicity 1 and its multiplicity is The Wronskian for the fundamental set of solutions to the DE ty" +2y" - y' + ty = 0 i a) ct² b) ct² c) ct d) ct¹ If x= is the complementary solution of the nonhomogeneo 3 -2 -21 then the particular solution of the system is 2 -2 a) x(t)= 80-2)+1(7)-(32) b) x²(t)= | c) + 1 10 9x0-11(7)-(12) 1 3/2 d) x³ (t) x0-90* 10 1 The residue Res (31) for the function R(z)=- a) i b) - 3i c) 2 d) 0 z-9 is (z²+9) The function (z) that is harmonic outside the unit circle|z|=1 that satisfies (e¹ª) = cos² 0, 0≤0≤27 such that 6 (re") → 1½ along all the large radii is a) (z) = Re b) 0(2)-Re()+ c) (z)= Re d) (z) = 2z2 (2)