solve(x^2-5=0,x);

solve({x+y=2,x-y=3},{x,y});

solve(exp(x)=6,x);

solve(sin(x)=x,x);

solve(cos(x)=x,x);

evalf(solve(cos(x)=x,x));

solve(sin(x)=1,x);

solve(x^2=-1,x);

diff(x/(1+x),x);

int(1/x,x);

int(1/(x*(1-x/K)),x);

dsolve( diff(N(t),t)=r*N(t)*(1-N(t)/K) );

dsolve( [ diff(N(t),t)=r*N(t)*(1-N(t)/K) , N(0)=N0 ] );

dsolve( [ diff(x(t),t)=y(t) , diff(y(t),t)=-x(t) , x(0)=x0 , y(0)=0 ] );

with(DEtools):

r:=2: K:=3:

DEplot( diff(N(t),t) = r*N(t)*(1-N(t)/K) , [N(t)], t=0..5, N=0..5);

DEplot( diff(N(t),t) = r*N(t)*(1-N(t)/K) , [N(t)], t=0..5, N=0..5 , [ [N(0)=1],[N(0)=2],[N(0)=4] ] );

DEplot( diff(N(t),t) = r*N(t)*(1-N(t)/K) , [N(t)], t=0..5, N=0..5 , [ [N(0)=1],[N(0)=2],[N(0)=4] ] , arrows=NONE, thickness=1, linecolor=red );

plot(sin(x),x=-6*Pi..6*Pi);

plot([cos(x),sin(x)],x=0..2*Pi);

plot([cos(x),sin(x),x=0..2*Pi]);

with(plots):

fieldplot([r*N*(1-N/K),0],N=-1..4,y=-1..1,grid=[20,3],arrows=thick);

implicitplot(x^2+y^2=1,x=-1.2..1.2,y=-1.2..1.2);

unassign('r');

implicitplot(0 = -x^3+r*x, r = -1 .. 1, x = -3 .. 3); 

implicitplot(0 = -x^3+r*x, r = -1 .. 1, x = -3 .. 3, gridrefine = 2); 


p1:=plot(sin(x),x=0..2*Pi,color=blue,linestyle=2):

p2:=plot(cos(x),x=0..2*Pi,color=black,linestyle=3):

display(p1,p2);

h:=10; unassign('r');

animate(plot,[ [r*x-x*x*x,-h],x=-5..5,color=[red,blue] ] , r=-1..20, frames=60);

unassign('r', 'h'); 

implicitplot3d(0=r*x-x*x*x+h,r=-1..1,h=-1..1,x=-3..3,grid=[25,25,25]);