Here are some Mathematica graphs for functions which arise on the first homework assignment.

f[c_, x_] := x/3  - 1/9  +  Exp[-2 x]  +  c Exp[3  x]

\(fntable\  = \ Table[f[i, \ x], \ {i, \(-5\), 5}]; 

    plottable\  = \ 
      Map[
		Plot[#, \ {x, \ \(-3\), 3}, 
			
            PlotRange -> \ {\(-10\), 10}, 
			\ 
            DisplayFunction -> 
				Identity]&, fntable]; 

    Show[plottable, \ DisplayFunction\  -> \ $DisplayFunction]\)

f[c_, x_] := (3/4) Cos[2 x] + (3/2) Sin[2 x] + (c/x)

\(fntable\  = \ Table[f[i, \ x], \ {i, \(-5\), 5}]; 

    plottable\  = \ 
      Map[
		Plot[#, \ {x, \ \(-10\), 10}, 
			
            PlotRange -> \ {\(-10\), 10}, 
			\ 
            DisplayFunction -> 
				Identity]&, fntable]; 

    Show[plottable, \ DisplayFunction\  -> \ $DisplayFunction]\)

f[a_, x_] := -3 Exp[x/3]  +  (a  +  3) Exp[x/2]

\(fntable\  = \ Table[f[i, \ x], \ {i, \(-5\), 5}]; 

    plottable\  = \ 
      Map[
		Plot[#, \ {x, \ \(-10\), 10}, 
			
            PlotRange -> \ {\(-10\), 10}, 
			\ 
            DisplayFunction -> 
				Identity]&, fntable]; 

    Show[plottable, \ DisplayFunction\  -> \ $DisplayFunction]\)

\(Plot[{
        12 + 8\/65\ \((Cos[2\ t] + 8\ Sin[2\ t])\) - 
          788\/65\ Exp[\(-\(t\/4\)\)], 
		12}, 
	{t, \ \(-1\), \ 20}]\)

\(Plot[{2, \ Exp[\((1/10)\) t\  + \ Sin[t]/5], \ 
		
        Exp[\((1/10)\) t]}, \ 
	{t, 0, 10}, Axes -> True
	\ ]\)

\(Plot[{2, \ Exp[\((1/10)\) t\  + \ Sin[t]/5], \ 
		
        Exp[\((1/10)\) t]}, \ 
	{t, 0, 50}, Axes -> True
	\ ]\)

N[10  Log[2]]

Plot[{2, Exp[(t/10) + (1/5) Sin[2 π t]], Exp[(t/10)]}, {t, 0, 10}, 
      Axes -> True]

Plot[{2, Exp[(t/10) + (1/5) Sin[2 π t]], Exp[(t/10)]}, {t, 0, 75}, 
      Axes -> True]