I need the simulation as a proof of this answer using any mathematical software

Q2 A system is given by a circuit network as shown in Figure Q2. R1 = 20 R3 = 40 ir iz E(t) = - 10e2 R2= 20 L = 11 C = 0.5F HE Figure Q2 (a) Show that the linear differential equations for the system are given by, (1) = 0.511 -3i2 +562 1 (t) = 2i1-62 6) By considering the initial conditions, i,(0)=-120=1, calculate the particular solution of the linear differential equations system 2.12 0 4.12 -10e IH 2.12 0.58 2) At node - Vielt) - 4 izlt) + 1. diz 4 iz(t) + diz 0 at and -24 - loe 2 cilt) + 2 (1,-42) + 1 0.5 se; (t) at differentiating to both the sides 20 e 4 dij dt 2 di at 2 ilt) Viz(t) = 2 ( lilt)exit)) 2) - 2 lact) by eq" - 04 2 lit) - 2 izlt) = 4 dilt) + diz dt diz 2 eilt) 6 iz It) dt by eq?- + 20 e e 27 4 di, dt 2x2 4,(t) 12.421t) + 2 iilt) 4 dis 2 lt) - 12 iz It) + 20e . e27 0.5 filt) -6(1 + 5 e 5e27 at dii -zt 0.5 dilt) - 3 iz(t + 5 dt diz dt 2 lit) - bez it) (b) (0) = - (20) = 1 - dir dt 0.5 eilt) - 3 iz(t) + 50 2t by laplece S.[, (S) llo) 0.5 LIS) - 3 Iz(s) + 5 (5+2) (5-0.5) 1,(s) + 3 12 (s) 1+ 5 S+2 S+7 S+2 and diz at 2 eilt) - 6 dalt) S 6218) ezlo) 2 fils) - 6 fe(s) 2 fils) (5+6) 12(5) -1 = [2 (s) 2 Fis) + 1 (5+6) (5-0.5) C1s) + 6 Fils) + 3 (5+6) St7 (5+2) 1,(s) (5-0.5) (5+6) + 6 S+7 [ 3 (S+6) St2 S +6 (s) a (5+7) (5+6) 315+2) (5+2) ( S2+ 5.55 -3 +6) I, (s) S105+36 (5+2) (52+5.55 +3) and (5-0.5) ((s+6) fzls)-1] + 31215) a 5+7 2 S+2 [z(s) (5-0.5) (5+6) + 6 669/ (5-0.5)(5+2)+5+7) (5+2) 2 I (S) = 2 [ $? +1.55 -/+s+7] (5+2) ( 52+5.53-3+6) 2 (52+2-55+6) (5+2)(5275-55+3) Sw*-**-** .] - 15624 coy 173 16 et eilt) = + 7/73 584 sin +] - is