Question

10–15 IVPs Solve the following initial value problems. 10. yı = -4yı + 5y2 yż = -yı + 2y2 Yı(0) = 0, y2(0) = 4

Answer 1

. 10 fet A=1 1-4 57 The characteristie polynomical of Ais A(1) = 72-lfaceA)+ delt =4*+21-3 A1A)=0 => 72+27-3=0 => 6+3)(2-1) = 0 fet d =-3 and 2q = 1 Telgenvector of A Corresponding to a = -3. (A+31)y = 0 (1+0) 1- 59 R, → Re-Ri : ra+5b=0 R Let b=1 then a=5 -Eigenvector of A Corresponding to 9 = 1 (A-I) V2 = 0 , V2 + 0) -5 5110 109 Hot non Rey Rq u tri Të öllum 1-5 51a 02.

5a45b=0 fel b=1, then a=!! ! : ) General solution of the given System is your soul - gent as ek nie -34 t7 5ge the 34 it TGE + Gel 56+4 = 0=> -1, 6 - 85 G + C = 45 Ylt)= 18, (+)] 1-50-34+ 5eti... [Yelts] Test 4 56 t ] Hence Y, (t) = 15 let_ e 3t), el 8, lt) = 5et-e-st1