2+2

a=2

b=3

a*b

a=4

c=20

ab

a*b

Clear[a,b]

a*b

Sin[Pi]

∫E^t\[DifferentialD]t

Integrate[E^t,t]

a

b

c

Clear["Global`*"]

a

b

c

(*this is a comment*)

ρ

Integrate[ρ^2,ρ]

f[x_] = x^3

g[x_] = a*x^4

Plot[f[x],{x,-3,3}]

g[x_] = Exp[-x^2]

Plot[{f[x],g[x]},{x,-3,3}]

Plot[{f[x],g[x]},{x,-3,3},PlotStyle->{Red,Blue}]

Plot[{f[x],g[x]},{x,-3,3},PlotStyle->{Red,Blue},PlotRange->{{-2,3},{-2,1.5}}]

Plot[x^2,{x,0,1}]

VectorPlot[{x,y},{x,-3,3},{y,-3,3}]

VectorPlot[{x^2,x*y},{x,-3,3},{y,-3,3}]

yprime = -(1/2)*y +(1/2)*Exp[x/3]

VectorPlot[{1,yprime},{x,-3,3},{y,-3,3}]

vplot = VectorPlot[{1,yprime},{x,-3,3},{y,-3,3},VectorScale->{0.04,0.04,None},Axes->True]

f[t_] = (3/5)*Exp[t/3] + Exp[-t/2]

solplot = Plot[f[t],{t,-3,3},PlotStyle->{Red}]

Show[vplot,solplot]

Out[52]

Out[59]*7

f[t]

f[t_,c_] = (3/5)*Exp[t/3] + c*Exp[-t/2]

Table[f[t,c],{c,-8,4,2}]

solplot2 = Plot[Evaluate[Table[f[t,c],{c,-8,4,2}]],{t,-3,3},Axes->True]

Show[vplot,solplot2]

diffeq = y'[x]== -(1/2)*y[x] +(1/2)*Exp[x/3]

DSolve[diffeq,y,x]

f[x]

D[f[x],x]

Clear[g]

g[x_] = x^3

D[g[x],{x,2}]

Clear[f]

f[x_,y_] = 3E^x*y^3

Integrate[g[x],x]

Integrate[g[x],{x,0,1}]

ContourPlot[-x^3 + 3*y - y^3 ==1, {x,-3,3}, {y,-3,3}]

g[x_,y_,c_] = -x^3 + 3*y - y^3 -c

ContourPlot[g[x,y,2]==0,{x,-3,3},{y,-3,3}]

Table[g[x,y,c],{c,-6,6,2}]

ContourPlot[Evaluate[Table[g[x,y,c]==0,{c,-8,8,2}]],{x,-3,3},{y,-3,3},PlotPoints->40]

curveplot = ContourPlot[Evaluate[Table[g[x,y,c]==0,{c,-20,20,4}]],{x,-3,3},{y,-3,3}]

vplot = VectorPlot[{1,x^2/(1 - y^2)},{x,-3,3},{y,-3,3},VectorScale->{0.04,0.04,None},Axes->True]

Show[vplot, curveplot]