SetDirectory[NotebookDirectory[]];

DSolve[NN'[t]==-lambda*NN[t],NN[t],t][[1]][[1]]

yanl[t_]:=1;C1=10^(23);
Plot[yanl[t],{t,0,2Thalf}]

N0=10^(23);lambda=0.1;Thalf=Log[2]/lambda;
s=NDSolve[{NN'[t]==-lambda*NN[t],NN[0]==N0},NN,{t,0,2Thalf}];

Plot[Evaluate[NN[t]/.s],{t,0,2Thalf},PlotRange->All]

s

y[t_]:=Evaluate[NN[t]/.s][[1]];
Plot[y[t],{t,0,Thalf}]