Question

1. Given the differential equation da + 2x = 12-<+1, x(1) dt the value of x(2) is 87 91 b) 48 48 a) c) 33 16 d) 33 16 e) None of these Ķ CLETA ution

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Answer 1

Option e is correct answer which is none of these.
solution:- + da +2x . . + *(1) = 1 at > da t t dt 2 spat- sz zlogt at a e e da et 2x { x = t-It This is linear differential equation of first order. dx + Px = 0 P = 22 Q = t-1+ Integrating factor (1.4) solution :- K. (.F-) = SQ (15.) et +C = [(4-14 uted to X. (J.F.) = 1143-%' + t) et +C Ę + using boundary condition:- & 3 t. de te 4+' 4 X. t² t 4 3 x(1) = Ź 2 C- 2 CE - 3 + 4 12 ta ) Ca x. t² AITO € + t2 2 - 3 + ² + t2t² Now putting t=2. 212)=4 - } + { + 58 = Now 48-32 + 24 +1 48 41 48 -