Question

.2 4. Find the solutions of the following initial value problems. a. de = Xx(1) = 2 yat=x+ at b. tax = te i+x, x(2) = 4 A chemical reaction is noored t3

Answer 1

- 2 + xt 2. V ) 2 evt. by 0 $ + + av = V2 + y at 3 = sono state 2 t = logeth les a lot tej st.) 7 Vien now x(1)=2 x=2, t=1 - 1 l = log 1 to lutt the value ofc in 2 is Fa ( 2 ) = logt - 16 Answers

® Similarly tax t e X1t ta at devide t both side now » av t putt get diff. it x=vt awe now it wir.tot in now putt in now Putt v dn = dx = uttal or y tay len = e ty

Saya fal Integrate it Se du = logt to [e = logt to v=2 xlt 1. e = logt tc 2 - log (logt te) - x(2)=4 ; x=4 ; t=2 tot eng (log & te) 2 = log (eog2tc) loge + c = e² [e² loge = c now putt the value of Meta Long (lingt + e"-hegy Anus Awe qe te lang (heng ftem in
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