ve[t_]:=(4/10) Sin[200 Pi t];
v23[t_]=β (Exp[(v2[t]-v3[t])/.026]-1);

node1=c1 (v2'[t]-v1'[t])==v1[t]/r0-ve[t]/r0;
node2=c1(v1'[t]-v2'[t])==(1-α)v23[t]+v2 [t]/r1+v2[t]/r2-vb/r2;
node3=c2 v3'[t]==v23[t]-v3[t]/r3;
node4=c3(v4'[t]-v5'[t])==vb/r4-v4[t]/r4-α v23[t];
node5=c3(v4'[t]-v5'[t])==v5[t]/r5;
ics={v1[0]==0,v2[0]==vb/2,v3[0]==vb/2,v4[0]==vb,v5[0]==0};

params={vb->6,r0->1000,r1->9000,r2->9000,r3->9000,r4->9000,r5->9000,α->99/100,β->10^-6,c1->10^-6,c2->2 10^-6,c3->3 10^-6};

transistorSol=NDSolve[{node1,node2,node3,node4,node5,ics}/.params,{v1,v2,v3,v4,v5},{t,0,0.2},Method->{"EquationSimplification"->"Residual"},MaxSteps->100000] ;

Plot[Evaluate[{v3[t],v4[t]}/.transistorSol],{t,0,0.2},PlotRange->All,ImageSize->400, PlotLegends->{Style["Node 3",14], Style["Node 4",14]}, Frame->True,FrameLabel->{Style["Time",18],Style["Voltage (V)",18]}]