Question

Problem 1 Determine a particular solution for the systems described by the following differential equation u(e) + 4y(t) = 3 =(), for the following inputs: 1. o(t)=t 2. x(t) = et 3. 2(t) = cos(t) + sin(t)

Answer 1

7167 + 4 ylt)= 3 x1t) (D*+ 4) ylt) = 3D elt) where or a ver (11 :7 particelar solution Upltls ret? upiter = t - - bitu Hehe altro t e Halamat pols 7 :La-) scu 71---(ca) saal) [o-o-7] © 2) = ét PL) = e xt) 00) ku tohen selfie eat while I at opless t fla) flea? #0 .

Ee QE+ f(0) et | Xple) - et t particular solution X(t) = Cost & sint When alt) = sin(at) f(+2²) to sinat f (a) cost tsiuk of (D) cost siut o fD f(0) 191 Cost Sint putu Dtu cort + siut -1 + 1. Itu apltls 1/3 [ cost+ siut]