(** EQUAZIONI NONLINEARI **)

Clear[f,g,a,a0];
f[x_]:=Sin[x];
g[x_]:=a*x;
a0=0.1;
Plot[{f[x],g[x]/.a->a0},{x,-Pi,Pi},PlotRange->{{-Pi,Pi},{-1,1}},PlotStyle->{{RGBColor[0,0,1],Thickness[0.01]},{RGBColor[1,0,0],Thickness[0.01]}}]

Clear[ff,a0];
ff[1][x_]:=f[x];
Do[a0=(i-1)*0.4;ff[i][x_]=g[x]/.a->a0,{i,2,5}]

a0=0.;
i=1;
While[a0≤2.,{pl[i]=Plot[{f[x],g[x]/.a->a0},{x,-Pi,Pi},PlotRange->{{-Pi,Pi},{-1,1}},PlotStyle->{{RGBColor[0,0,1],Thickness[0.01]},{RGBColor[1,0,0],Thickness[0.01]}}];i+=1;a0+=0.4}];

Show[pl[2]]

Clear[a0];
Animate[Plot[{f[x],g[x]/.a->a0},{x,-Pi,Pi},PlotRange->{{-Pi,Pi},{-1,1}},PlotStyle->{{RGBColor[0,0,1],Thickness[0.01]},{RGBColor[1,0,0],Thickness[0.01]}}],{a0,0,2},AnimationRunning->False]

Clear[f1,g1];
f1[x_]:=Exp[-x];
g1[x_]:=x^3;
Plot[{f1[x],g1[x]},{x,0,2},PlotRange->{0,2},PlotStyle->{{RGBColor[0,0,1],Thickness[0.01]},{RGBColor[1,0,0],Thickness[0.01]}}]

Clear[f2];
f2[x_]:=Exp[-x]-1/2;
Plot[f2[x],{x,0,2},PlotRange->{-1/2,1/2},PlotStyle->{{RGBColor[0,0,1],Thickness[0.01]}}]