## 535 Reputation

17 years, 95 days

## A solution......

Here is just arbitrarily chose the range 0 <= t <= 5.

## numpoints...

Try using the numpoints option in the plot command as follows:

plot(sin(x),x=0..2*Pi,numpoints=1000)

You may try a larger value than 1000 if necessary.

## Tautology...

The inequality is true for all values of x.

## DEplot will work...

`Try this:`
`> with(DETools);> DEplot((D(u))(t) = -u(t)^5+u(t)^3-u(t)^2, u(t), t = -5 .. 5, u = -5 .. 5, arrows = medium);`

## exp() not e^...

Maple does not recognize e^(y/x) as the exponential function. You have to use exp(y/x).

## Using the map command...

Since you mentioned having difficulty using, in particular, the map command, here is one way your problem can be solved:

F:=x->Matrix([[x,x^2],[exp(x),sin(x)]]):

FF:=unapply(map(diff,A(x),x),x):

This allows you to do, for example, F(0) and F'(0), and get the expected matrices.

## Use implicitplot...

Try this:

with(plots):

implicitplot(x^2+(y-3)^2=25,x=-10..10,y=-10..10,numpoints=1000)

## Use simplify...

simplify((3*h^2+12*h)/h)

## Try this.....

restart

with(plots):

K:=(V,E)->E*log(V):

P:=(V,E)->E+V*log(V):

plot3d({K(V,E),P(V,E)},V=0..20,E=0..190)

with(DETools):

A simply fix would be to change all instances of \[ ... \] in your LaTeX code to \( ... \) (or \$ ... \$) if you prefer. \[ ... \] creates displaymath which is centered, whereas \( ... \) creates inline math which is not centered.

## Here's a 2-d example...

The following command generates the phase portrait along with the trajectory of the solution satisfying the condition x(0)=-1, y(0)=2.

with(DETools):

DEplot({(D(x))(t) = x(t)-y(t)^2, (D(y))(t) = x(t)*(D(y))(t)+2*y(t)}, {x(t), y(t)}, t = 0 .. 5,x = -5 .. 5, y = -5 .. 5, arrows = medium, [[0, -1, 2]]);

Hope this gets you in the right direction.

## Try this using Array...

with(plots):

A:=Array(1..3,1..1):

A[1,1]:=plot(x,x=0..0.25):

A[2,1]:=plot(x^2,x=0..0.25):

A[3,1]:=plot(x^3,x=0..0.25):

display(A)

## Explicitly defined functions......

plota:=plot(x,x=-1/2..0):

plotb:=plot(x^2,x=-1/2..0):

plotc:=plot(x^3,x=0..1/2):

plotd:=plot(x^4,x=0..1/2):

plots:-display({plota,plotb,plotc,plotd})

## Try this...

`> dsolve({(D(x))(t) = 2*x(t)-2*z(t), (D(y))(t) = 2*y(t)+2*z(t), (D(z))(t) = -2*x(t)+2*y(t)+4*z(t)}, {x(t), y(t), z(t)});          /             1                                       { x(t) = _C2 - - _C3 exp(6 t) + exp(2 t) _C1,           \             2                                                1                                               y(t) = - _C3 exp(6 t) - _C2 + exp(2 t) _C1,                   2                                                                        \            z(t) = _C2 + _C3 exp(6 t) }                                    / `
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