l1=(-3+Sqrt[5.])/2;l2=(-3-Sqrt[5.])/2;

l1*l2

l1+l2

g[u_]:=UnitStep[u]*(Exp[l2*u]-Exp[l1*u])/(l2-l1)

Plot[g[u],{u,-2,12},AxesLabel->{"u","g(u)"}]