Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

after solved, 

diff(a(t), t) = diff(a(t), t)

diff(b(t), t) = 0

diff(c(t), t) = -b(t)/c(t)


there is a diff(a(t), t) term 

how to plot this kind of system?

can diff(a(t), t) be ignore so that only consider two equations, diff(b(t),t) and diff(c(t),t) ?

if so, i use below to plot, it can not show the arrow clearing , i can only see arrow near origin, but not far point

fieldplot([0, y/x], x = -2 .. 2, y = -2 .. 2);
fieldplot([0, y/x], x = -2 .. 2, y = -2 .. 2, arrows = SLIM,grid = [1, 1]);
fieldplot([0, y/x], x = -10 .. 10, y = -10 .. 10);

 about how to calculate vector field of system of 3 differential equations which in terms of a(t), b(t), c(t) , diff(a(t),t), diff(b(t),t), diff(c(t),t)?

is the only method is the express diff(a(t),t), diff(b(t),t), diff(c(t),t) in terms of a(t), b(t), c(t) ?

for example 

<diff(a(t),t), diff(b(t),t), diff(c(t),t)>

if result is

diff(a(t),t) = a(t)*b(t)

diff(b(t),t) =b(t)*c(t)

diff(c(t),t) =c(t)*a(t)

<a(t)*b(t), b(t)*c(t), c(t)*a(t)>


is it the vector field <a*b, b*c, c*a> ?


sys := {diff(b(t),t) = 0,diff(c(t),t) = -b(t)/a(t)};
DEplot(sys, [b(t),c(t)], t=0..5, x=-5..5, y=-5..5);
Error, (in DEtools/DEplot) Option keyword (x) was not in the allowed set of options, consisting of: iterations, arrows, dirgrid, obsrange, scene, colour, linecolour, stepsize, a dependent variable range, a list of initial conditions or one of the allowed plot options: {animate, axes, color, colour, coords, font, scaling, style, symbol, title, view, animatecurves, animatefield, axesfont, dirfield, labelfont, linestyle, numframes, resolution, thickness, tickmarks, titlefont, xtickmarks, ytickmarks}, or one of the allowed dsolve/numeric options: {abserr, control, ctrl, initial, itask, maxder, maxfun, maxkop, maxord, maxpts, maxstep, method, mi..

diff(a(t), t) = diff(a(t), t);
diff(b(t),t) = 0;
diff(c(t),t) = -b(t)/a(t);

[diff(rhs(sol[1][2]), a(t)),diff(rhs(sol[1][2]), b(t)),diff(rhs(sol[1][2]), c(t))];
Error, (in VectorCalculus:-diff) invalid input: diff received a(t), which is not valid for its 2nd argument




eq2 := b(t)*(diff(c(t), t))*(diff(a(t), t))+b(t)*(diff(a(t), t))+a(t)*(diff(c(t), t));
eq3 := a(t)*(diff(b(t), t))(diff(a(t), t))+b(t)*(diff(b(t), t))*(diff(c(t), t));
eq4 := b(t)*(diff(c(t), t))(diff(b(t), t))+a(t)*(diff(b(t), t))+b(t)*(diff(c(t), t));
eq2a := eval(subs(c(t)=exp(t), eq2));
eq3a := eval(subs(c(t)=exp(t), eq3));
eq4a := eval(subs(c(t)=exp(t), eq4));
dfieldplot([eq2a,eq3a], [a(t), b(t)], t = -5 .. 5, a = -5 .. 5, b = -5 .. 5, arrows = SLIM, color = black, dirfield = [10, 10]);


I think I found a bug concerning the useage of assume and alias:



a, b
















Commenting out the alias command produces correct results. I am on linux with build 922027.

 from determinant's polynomial?                                                                                                       

I am trying to find a general solution to the 1D-wave equation


pdsolve(Eq1,HINT=f(x)*g(t)); # Hinting pdsolve gives general solution using separation of variables

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)}); # without HINT and using intial conditions, I get travelling wave solution

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)},HINT=f(x)*g(t)); # Now when I try to use hint and ICs both, pdsolve return nothing.

I want to use separation of variables to find solution to the wave equation.

Any comment?


without _Y(t) and DESol?

f := diff(u(t), t$2) + (2/t-1/t^2*p(1/t))*diff(u(t),t) + 1/t^4*q(1/t)*u(t) = 0;
u(t) = DESol({q(1/t)*_Y(t)/t^4+(2/t-p(1/t)/t^2)*(diff(_Y(t), t))+diff(_Y(t), t, t)}, {_Y(t)})

just would like to find u1 and u2 solution

 from galois group function's result?                                     

g[1] := (diff(a(t), t))/(t^2-1) = 1;
g[2] := (diff(a(t), t))*(diff(b(t), t)) = 1;
dsolve({eq2, eq3});
sys := DiffEquation([g[1]=1, g[2]=1], inputvariable = [b(t)], outputvariable = [a(t), b(t)]):
ts := 0.1:
t_sim := 10.0:
#in_t := Sine(1, 1, 0, 0):
#in_z := Sine(1, 1, 0, 0, samplecount = round(t_sim/ts), sampletime = ts, discrete):
in_t := t:
sol := Simulate(sys, [in_t]):
p1 := plots[odeplot](sol, [[t, a(t)]], t = 0 .. t_sim, numpoints = 200, color = red):
Error, (in DEtools/convertsys) unable to convert to an explicit first-order system
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

would like to draw the graph of x^2-1

with below sys instead of x^2-1 

sys := {-(1/2)*(-x-1+sqrt(-3*x^2-2*x-3))*(diff(y(a, b), b))/x^2+(diff(y(a, b), a))*(diff(y(a, b), b)), (1/2)*(x+1+sqrt(-3*x^2-2*x-3))*(diff(y(a, b), a))/x^2+(x^2+x+1)/x^4, (1/2)*(x+1+sqrt(-3*x^2-2*x-3))*(diff(y(a, b), a))/x^2-(1/2)*(-x-1+sqrt(-3*x^2-2*x-3))*(diff(y(a, b), b))/x^2+(x^2+x+1)/x^4};


I'm having trouble with using constrained optimization to solve a problem.

The problem is set up as:

Max: w=x1/2 y1/4

Subject to: K=x+4. K is a constant.


I'm not sure where to start.

 from permutation group to permutation group and inverse this mapping?

how to do?

how to find [[1,3,2,4],[1,2]] and [2,3][[1,3,2,4],[1,2]] and [2,4],[[1,3,2,4],[1,2]]?

and why Orbits(G) put permutation group into power, how to display the result of this power group?

i use this or quartic polynomials' resolvent

G := SpecialUnitaryGroup(3, 1);

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