before run file remove all (:) i want calculate equation but with a condition for example: when a=4 then find other parameter in my equation with respect to a=4 find other

usesol.mw

when i finding parameter i want just choose a case for example a_1=a_1  and any other case a_2=0,and remove other case how i can do in maple

Download choose_case.mw

i am looking for simplify this type of simplifying assume beta is Real and there is any stuf package for working with complex and conjugate automaticaly

Download simplify.mw

Hi
i write my code for calculate this type of function but the result is so different from mine i  will post here i hope someone tell me where is problem

i have this

i want this

Download EX1.mw

Hi
i did calculation part by part of adomian laplace method but if we can make a loop for it is gonna be so great and take back a lot of time

for get definition use this pdf for fractional derivation

[Copyrighted material removed by moderator - see https://doi.org/10.4236/am.2018.94032]

Download solving_example_1.mw

Hi

i use other code for equation too when i use allvalues(Root(...)) it is more near but question is this why not satisfy the ode equation this is my equation this parameter are find for this ODe why not satisfy otherwise my equestions must be wrong!

same_equation_different_parameter.mw

display([plottools[arc]([op(coordinates(Omega))], r, t .. t + Pi/2, color = red, t4), plottools[arc]([op(coordinates(Omega))], r, t + Pi .. t + (3*Pi)/2, color = coral, t4), plottools[arc]([op(coordinates(Omega))], r, t - Pi/2 .. t, color = cyan, t4), plottools[arc]([op(coordinates(Omega))], r, t + Pi/2 .. t + Pi, color = green, t4)],
draw([Cir(color = blue, t4), cir(color = grey, t4), sT(color = black, t4), XXp(color = black, l3), YYp(color = black, l3), L1(color = black, l3), L2(color = black, l3), N1(color = blue, symbol = solidcircle, symbolsize = 15), N2(color = blue, symbol = solidcircle, symbolsize = 15), N3(color = blue, symbol = solidcircle, symbolsize = 15), M1(color = blue, symbol = solidcircle, symbolsize = 15)]), axes = none, view = [-30 .. 10, -10 .. 10], size = [800, 800])::
plots:-animate(Proc, [t], t = 0 .. 2*Pi, frames = 30).;

why the instruction concerning the arcs is not resected ? Thank you.

Download pde-solve.mw

restart;
Proc := proc(t) local t4, l3, R, r, eq, sol; _EnvHorizontalName := 'x'; _EnvVerticalName := 'y'; t4 := thickness = 4; l3 := linestyle = dot; R := 9; r := 1/2*R; geometry:-point(OO, 0, 0); geometry:-circle(Cir, [OO, R]); geometry:-point(K, R*cos(t), R*sin(t)); geometry:-point(Omega, r*cos(t), r*sin(t)); geometry:-circle(cir, [Omega, r]); eq := geometry:-Equation(cir); geometry:-line(XXp, y = 0); geometry:-line(YYp, x = 0); geometry:-line(L1, y = x); geometry:-line(L2, y = -x); geometry:-projection(M1, K, XXp); geometry:-coordinates(M1); geometry:-point(K2, geometry:-coordinates(M1)[1] - 2*R, 0); geometry:-coordinates(K2); geometry:-segment(sT, K2, M1); geometry:-point(N1, 0, R*sin(t)); subs(y = x, eq); sol := solve(%, x); geometry:-point(N2, sol[2], sol[2]); subs(y = -x, eq); sol := solve(%, x); geometry:-point(N3, sol[2], -sol[2]); plots:-display(geometry:-draw([Cir(color = blue, t4), cir(color = grey, t4), sT(color = black, t4), XXp(color = black, l3), YYp(color = black, l3), L1(color = black, l3), L2(color = black, l3), N1(color = blue, symbol = solidcircle, symbolsize = 15), N2(color = blue, symbol = solidcircle, symbolsize = 15), N3(color = blue, symbol = solidcircle, symbolsize = 15), M1(color = blue, symbol = solidcircle, symbolsize = 15)]), axes = none, view = [-30 .. 10, -10 .. 10], size = [800, 800]); end proc;
plots:-animate(Proc, [t], t = 0 .. 2*Pi, frames = 200);
NULL;
I am trying to program  this drawing, how to improve this code ? Thank you.

restart;
with(plots);
with(geometry);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
xA := 5;
yA := 0;
point(A, xA, yA);
xB := 5;
yB := -7;
point(B, xB, yB);
midpoint(C, A, B);
segment(sg1, A, B);
xP := -12;
yP := 0;
point(P, xP, yP);
PerpenBisector(L, C, P);
line(YYp, y = yB);
line(XXp, y = 0);
intersection(M, L, YYp);
line(PM, [P, M]);
projection(H, C, PM);
triangle(CMP, [C, M, P]);
triangle(ABH, [A, B, H]);
distance(B, H);
circle(cir, [B, 7]);
display(textplot([[coordinates(A)[], "A"], [coordinates(B)[], "B "], [coordinates(C)[], "C"], [coordinates(M)[], "M"], [coordinates(H)[], "H"], [coordinates(P)[], "P"]], align = {"above", 'right'}),
draw([YYp(color = red), XXp(color = black), PM(color = green), L(color = green), sg1(color = black), cir(color = magenta), P(color = black, symbol = solidcircle, symbolsize = 10), M(color = black, symbol = solidcircle, symbolsize = 10), H(color = black, symbol = solidcircle, symbolsize = 10), A(color = blue, symbol = solidcircle, symbolsize = 10), B(color = blue, symbol = solidcircle, symbolsize = 10), CMP(color = blue, filled = true, transparency = 0.8), ABH(color = red, filled = true, transparency = 0.8), C(color = blue, symbol = solidcircle, symbolsize = 10)]),
axes = none, view = [-15 .. 14, -15 .. 3]);
I want to change this figure when xP varies from -12 to 12; Is it possible to use Explore or animate ? Thank you.

Sq := proc(n::integer)
local aS, oS, aC, oC, s, dr, pc, u;
aS := -i/n;
oS := sum(1/s, s = 1 .. n);
aC := 1/2*aS;
oC := oS - 1/2*1/((n + 1)*n);
point(S, aS, oS); point(C, aC, oC);
MakeSquare(K, [S, 'center' = C]);
u := (x, i) -> sum(exp(-x*k)/k, k = 1 .. i);
pc := plot(u(x, n), x = 0 .. 4, color = green);
dr := draw([K]);
display({dr, pc});
end ;Sq(1);
Error, (in geometry:-draw) non-numeric coordinate encountered, cannot determine plot view
How to correct this procedure ?

When the limit approaches from left, the result must be zero. What cause the wrong? Will introducing an extra parameter M affect the result in W1?

Download limit.mwlimit.mw

eqn := B(n) = -sum(binomial(n + 1, k)*B(k), k = 0 .. n - 1)/(n + 1);
init := B(0) = 1, B(1) = -1/2;
sol := rsolve({eqn, init}, B(n));
Why doesn’t this give me any solution ? Thank you.

How to show that the angle QF2P remains constant when M moves on the ellipse ? Perhaps with Explore ?
restart;
with(plots);
with(geometry);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
x0 := 100;
y0 := 40;
a := 7;
b := 5;
c := sqrt(a^2 - b^2);
ellipse(el, x^2/a^2 + y^2/b^2 - 1);
point(F1, -c, 0);
point(F2, c, 0);
eq := simplify((a^2 - x0^2)*(y - y0)^2 + (b^2 - y0^2)*(x - x0)^2 + 2*x0*y0*(x - x0)*(y - y0)) = 0;
sol := solve({eq}, {y});
line(tang1, op(sol[1]));
line(tang2, op(sol[2]));
sol2 := op(solve({op(sol[1]), x^2/a^2 + y^2/b^2 - 1 = 0}, {x, y}));
xM2 := rhs(sol2[1]);
yM2 := rhs(sol2[2]);
point(A, xM2, yM2);
sol3 := op(solve({op(sol[2]), x^2/a^2 + y^2/b^2 - 1 = 0}, {x, y}));
xM3 := rhs(sol3[1]);
yM3 := rhs(sol3[2]);
point(B, xM3, yM3);
line(Pol, [A, B]);
simplify(Equation(Pol));
isolate(%, y);
xM := 4;
sol := solve({subs(x = xM, x^2/a^2 + y^2/b^2 - 1 = 0)}, {y});
yM := rhs(op(sol[1]));
point(M, xM, yM);
line(Tang, x*xM/a^2 + y*yM/b^2 - 1 = 0);
intersection(P, tang1, Tang);
intersection(Q, tang2, Tang);
line(PF2, [P, F2]);
line(QF2, [Q, F2]);
alpha := FindAngle(PF2, QF2);
arctan(alpha);
evalf(%);
display(textplot([[-c, 0, "F1"], [c, 0, "F2"], [coordinates(B)[], "B"], [coordinates(A)[], "A "], [coordinates(M)[], "M "], [coordinates(P)[], "P "], [coordinates(Q)[], "Q "]], align = {"above", 'right'}), draw([el(color = red), A(color = black, symbol = solidcircle, symbolsize = 16), PF2(color = brown), QF2(color = brown), B(color = black, symbol = solidcircle, symbolsize = 16), M(color = black, symbol = solidcircle, symbolsize = 16), P(color = black, symbol = solidcircle, symbolsize = 16), tang1(color = green), tang2(color = green), Tang(color = green), F1(color = blue, symbol = solidcircle, symbolsize = 16), Q(color = blue, symbol = solidcircle, symbolsize = 16), F2(color = red, symbol = solidcircle, symbolsize = 16)]), axes = none, view = [-7 .. 15, -7 .. 12]);

It seems like there exists a bug when taking the following limit in Maple (I tried Maple 2021):

If I run this command:
> evalf(limit(CylinderU(0,CylinderU(0,x)),x=0));
1.2722774800
the result is 1.2722774800, which seems to be incorrect.
;

However, when I run this command:
> evalf(CylinderU(0,limit(CylinderU(0,x),x=0)));
0.5456799403
the result is 0.5456799403, which seems to be correct.

Finally, when I run this command:
> evalf(CylinderU(0,CylinderU(0,0)));
0.5456799403
the result is 0.5456799403 which is also correct.

My expectation is that all three commands must return the same result, thus I consider this a bug.
I also run the following command in WolframAlpha
> limit ParabolicCylinderU(0,ParabolicCylinderU(0,x)) as x->0.0
and obtained the correct result 0.54568, confirming that in Maple this is evaluated incorrectly.

Would appreciate if anybody can confirm that this is a bug.

How such Maple bug should be reported?