MaplePrimes - answers and comments on Question, plot

odeplot

Robert Israel — Thu, 20 Aug 2009 20:40:42 Z

The command is odeplot, not odeplots.

If the system is third order or higher in X[5], dsol should provide values of that second derivative, and then odeplot
will be able to plot it. If not, you'd need to find an expression for the second derivative in terms of variables and their first derivatives. You can use rifsimp in the DEtools package to help with this. For example, consider this system:

> sys:= {D(x)(t)=y(t)^2 + x(t), (D@@2)(y)(t)=x(t)};
    ics:= {x(0) = 1, y(0) = 0, D(y)(0) = 0};
    
> DEtools[rifsimp](convert(sys union {(D@@2)(x)(t)=w(t)},diff),[[w],[x,y]]);

TABLE([Solved = [w(t) = 2*y(t)*diff(y(t),t)+y(t)^2+x(t), diff(y(t),`$`(t,2)) = x(t), diff(x(t),t) = y(t)^2+x(t)]])

> d2x:= subs(%[Solved], w(t));

d2x := 2*y(t)*diff(y(t),t)+y(t)^2+x(t)

> plots[odeplot](dsol, [t, d2x], t = 0 .. 1);

Hello Dsolve produces X[5]

nmani — Thu, 20 Aug 2009 22:13:26 Z

Hello

Dsolve produces X[5] and first derivative and second derivative of that the problem is I do not know what is maple comand to plot it

I mean I use

plots[odeplot](dsol, [t, (D(X[5]))(t)], 0 .. 5, numpoints = 250); to plot first derivative what is maple comand like this for second derivative

is it plots[odeplot](dsol, [t, (D^2(X[5]))(t)], 0 .. 5, numpoints = 250); or

plots[odeplot](dsol, [t, (D[1,1](X[5]))(t)], 0 .. 5, numpoints = 250);

Thanks

please see mt file

nmani — Sun, 23 Aug 2009 22:51:03 Z

Dear Robert,

Hello.

Hope you are fine.

I have a second order system and initial condition, when I solve, in the solution, I see just till first order which you wrote me, so I wanted to use your sugestion to have second order and plot that, but I see one error since in my system I have sin() and cos(), I came up with this by Sub but is there any way that I can use rifsimp without substitution?

I mean any maple command by DEtools[rifsimp](sys,vars,options) with special options.

please please take a look at my file.

Many thanksDownload 11301_que.mpl
View file details

Second derivative

Robert Israel — Mon, 24 Aug 2009 01:14:19 Z

By the way, you shouldn't use .mpl as the extension for a worksheet file. It should be .mw (or .mws for a Classic worksheet). The .mpl extension is for text files in the Maple language.

Since your system contains this second derivative, it's not necessary to use rifsimp: we can simply use solve.

> RedSys := {58.86000000*cos(X[9](t))*cos(X[5](t))-58.86000000*sin(X[9](t))*sin(
X[5](t))+9.040000000*diff(diff(X[9](t),t),t)+9.040000000*diff(diff(X[5](t),t),
t)+6.000000000*diff(diff(X[9](t),t),t)*cos(X[5](t))+6.000000000*sin(X[5](t))*
diff(X[9](t),t)^2 = 0., 58.86000000*cos(X[9](t))*cos(X[5](t))-58.86000000*sin(
X[9](t))*sin(X[5](t))+14.08000000*diff(diff(X[9](t),t),t)+9.040000000*diff(
diff(X[5](t),t),t)+12*diff(diff(X[9](t),t),t)*cos(X[5](t))-12.*diff(X[9](t),t)
*diff(X[5](t),t)*sin(X[5](t))+58.86000000*cos(X[9](t))+6.000000000*diff(diff(X
[5](t),t),t)*cos(X[5](t))-6.000000000*diff(X[5](t),t)^2*sin(X[5](t)) = 0.};
incons1 := {X[5](0) = 0, X[9](0) = 0, D(X[5])(0) = 0, D(X[9])(0) = 0};
dsol := dsolve(RedSys union incons1, numeric);
secondderivs:= solve(RedSys,{diff(X[5](t),t$2),diff(X[9](t),t$2)});
d2x5:=subs(secondderivs,diff(X[5](t),t$2));
plots[odeplot](dsol, [t, d2x5], t = 0 .. 5,numpoints=250);

OMG Silly

nmani — Mon, 24 Aug 2009 01:27:08 Z

OMG

Silly me

Thanks

Hello I am wroking in mws

nmani — Mon, 24 Aug 2009 01:33:08 Z

Hello

I am wroking in mws but I saved to mpl to send you, does it have a problem

any way thanksss