Maple 2020 Questions and Posts

These are Posts and Questions associated with the product, Maple 2020

1) the two cylinders are centered on the x and z axis respectively

2) any two intersecting cylinders

Hi,

I want to define the functions 10 and 11 and then put them in the eq equation, then simplify them and get the unknown values after the solve command, but there are error.

And value the function psi ?

NULL

NULL

restart

with(student)

NULL

"U(xi[n]):=a[0]+sum(-a[i]*psi^(i)(xi[n]),i=1..1)+sum(-b[i]*psi^(-i)(xi[n]),i=1..1)+sum(-c[i]*((diff(psi,xi[n])^(i)))/(psi^(i)(xi[n])),i=1..1);"

Error, empty script base

Typesetting:-mambiguous(Typesetting:-mrow(Typesetting:-mi("U", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ξ", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", font_style_name = "2D Input", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo("≔", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("a", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mn("0", mathvariant = "normal"), open = "[", close = "]", mathvariant = "normal"), Typesetting:-mo("+", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("sum", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("&uminus0;", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("a", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", mathvariant = "normal"), Typesetting:-mo("⋅", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msup(Typesetting:-mi("ψ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ξ", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.3333333em", separator = "true", stretchy = "false", symmetric = "false"), Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("=", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(".", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mo(".", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo("+", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("sum", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("&uminus0;", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("b", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", mathvariant = "normal"), Typesetting:-mo("⋅", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msup(Typesetting:-mi("ψ", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mo("&uminus0;", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic")), superscriptshift = "0"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ξ", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.3333333em", separator = "true", stretchy = "false", symmetric = "false"), Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("=", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(".", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mo(".", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo("+", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("sum", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("&uminus0;", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("c", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("⋅", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfrac(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("diff", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ψ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mo(",", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.3333333em", separator = "true", stretchy = "false", symmetric = "false"), Typesetting:-mi("ξ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mambiguous(Typesetting:-msup(Typesetting:-merror("?"), Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0"), Typesetting:-merror("empty script base"))), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("ψ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ξ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal")), bevelled = "false", denomalign = "center", linethickness = "1", numalign = "center"), Typesetting:-mo(",", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.3333333em", separator = "true", stretchy = "false", symmetric = "false"), Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("=", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(".", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mo(".", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(";", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "true", stretchy = "false", symmetric = "false")))

 

NULL

U(xi[n+1]) := U(xi[n]+d)

U(xi[n]+d)

(1)

U(xi[n-1]) := U(xi[n]-d)

U(xi[n]-d)

(2)

NULL

eq := c*(diff(U, xi[n]))*(U(xi[n])+u(xi[n-1]))*(U(xi[n])+u(xi[n+1]))-(2*(u(xi[n-1])-u(xi[n+1])))*(U(xi[n])^2)(1-U(xi[n])^2)

-2*(u(xi[n-1])-u(xi[n+1]))*(U(xi[n]))(1-U(xi[n])^2)^2

(3)

NULL

Download abs.mw

 

the graf that I want to generate is like this one 

Hei

Vet noen om Windows 11 støtter Maple 2020? Eller støttes det bare av Windows 10.

I learned about Dodgson calculation of the determinant only recently (https://en.m.wikipedia.org/wiki/Dodgson_condensation).
I am only interested in symbolic expressions of the determinant.
Furthermore, I compared several methods. Not surprisingly, the build in method is the fastest. But why is the seq method slower than the proc method for the Dodgson method? Is there anything I could do to program it more efficiently?
 

restart; with(LinearAlgebra)

with(combinat); with(GroupTheory)

DetDef := proc (A) local i, n, sigma; description "Jeremy Johnson. Downloaded from https://www.cs.drexel.edu/~jjohnson/2016-17/winter/cs300/lectures/determinant.mw"; n := RowDimension(A); add(PermParity(Perm(sigma))*mul(A[i, sigma[i]], i = 1 .. n), `in`(sigma, permute([`$`(1 .. n)]))) end proc

InnerMatrix := proc (M::Matrix) SubMatrix(M, 2 .. RowDimension(M)-1, 2 .. ColumnDimension(M)-1) end proc

MatrixDet := proc (M::Matrix) local C, n, i, j; n := RowDimension(M)-1; C := Matrix(n, n); seq(seq(assign('C[i, j]', Determinant(M([i, i+1], [j, j+1]))), j = 1 .. n), i = 1 .. n); return C end proc

Dodgson := proc(M::Matrix)
 MatrixDet(M);
InnerMatrix(M) ^~ (-1) *~ MatrixDet(MatrixDet(M));
do if 1 < RowDimension(%) then InnerMatrix(`%%`) ^~ (-1) *~ MatrixDet(%);
end if;
until RowDimension(%) = 1;
Trace(%):
end proc:

Dodgsonseq := proc (E::Matrix) local w, dim, Z; dim := RowDimension(E); Z[dim] := E; Z[dim-1] := MatrixDet(E); Z[dim-2] := `~`[`*`](`~`[`^`](InnerMatrix(E), -1), MatrixDet(MatrixDet(E))); seq(assign('Z[w-1]', `~`[`*`](`~`[`^`](InnerMatrix(Z[w+1]), -1), MatrixDet(Z[w]))), w = dim-1 .. 1, -1); Trace(Z[1]) end proc

LaPlace := proc (M::Matrix) local c; add((-1)^(c+1)*M[1, c]*Minor(M, 1, c), c = 1 .. ColumnDimension(M)) end proc

dim := 7; A := Matrix(dim, dim, shape = symmetric, symbol = a)

7

(1)

start_time := time(); st := time[real](); Det1 := abs(A); CPUtime_used_Build_in_Determinant := time()-start_time; REALtime_used_Build_in_Determinant := time[real]()-st; start_time := time(); st := time[real](); Det2 := DetDef(A); CPUtime_used_Jeremy_Johnson_Determinant := time()-start_time; REALtime_used_Jeremy_Johnson_Determinant := time[real]()-st; start_time := time(); st := time[real](); Det3 := Dodgsonseq(A); CPUtime_usedDodgsonseq := time()-start_time; REALCPUtime_usedDodgsonseq := time[real]()-st; start_time := time(); st := time[real](); Det4 := Dodgson(A); CPUtime_usedDodgson := time()-start_time; REALtime_usedDodgson := time[real]()-st; start_time := time(); st := time[real](); Det5 := LaPlace(A); CPUtime_usedLaPlace := time()-start_time; REALtime_usedLaPlace := time[real]()-st; simplify(Det1-Det2); simplify(Det1-Det3); simplify(Det1-Det4); simplify(Det1-Det5)
``

0.32e-1

 

0.34e-1

 

0.93e-1

 

.108

 

47.094

 

41.295

 

40.766

 

38.158

 

0.31e-1

 

0.50e-1

 

0

 

0

 

0

 

0

(2)

Download test_Determinants_symbolic.mw

Just need some help using URL:-Get

Get("https://sdo.gsfc.nasa.gov/assets/img/browse/2023/05/05/20230505 _184918_512_0304.jpg")

I'm sure there are some tags to use but not sure how.  The site does show a script on best practices, but at the moment don't know how to apply them.  Can anyone offer some help?

As an example, the second display in the web site below shows the 42 possible triangulations of a cyclic heptagon polygon.

https://en.wikipedia.org/wiki/Polygon_triangulation

Hello,

I am trying to evaluate this expression numerically or symbolically without success.

> sum(1/(4.0*n^2-4*n+4*100000000^2+1)/10^n,n=1..infinity);

Maple is having hard time to convert it to LerchPhi and even more to evalf(%);

PS : mathematica is doing it at any precision very fast or can translate this into hypegoemetric.

PS2 : I use maple 2020 on windows 10 64 bits.

Is there any simple way that the colored shape created in the xy plane by the uploaded code can be projected in the z direction onto the surface of the unit sphere centred at the origin?

Projection.mw

hi,

What command can I use to solve the attached equation and draw its graph?

ode := -(q2-q4)*(q2-q3)*(q1-q4)*(q1-q3)*y(w)^2+(q1+q2-q3-q4)*(2*q1*q2-q1*q3-q1*q4-q2*q3-q2*q4+2*q3*q4)*(diff(y(w), w))*y(w)+(-2*q1^2-2*q1*q2+3*q1*q3+3*q1*q4-2*q2^2+3*q2*q3+3*q2*q4-6*q3*q4)*(diff(y(w), w))^2+(q1-q2+q3-q4)*(q1-q2-q3+q4)*(diff(y(w), w, w))*y(w)+(3*q1+3*q2-3*q3-3*q4)*(diff(y(w), w, w))*(diff(y(w), w))-3*(diff(y(w), w, w))^2+(-q1-q2+q3+q4)*(diff(y(w), w, w, w))*y(w)+2*(diff(y(w), w, w, w))*(diff(y(w), w)) = 0

-(q2-q4)*(q2-q3)*(q1-q4)*(q1-q3)*y(w)^2+(q1+q2-q3-q4)*(2*q1*q2-q1*q3-q1*q4-q2*q3-q2*q4+2*q3*q4)*(diff(y(w), w))*y(w)+(-2*q1^2-2*q1*q2+3*q1*q3+3*q1*q4-2*q2^2+3*q2*q3+3*q2*q4-6*q3*q4)*(diff(y(w), w))^2+(q1-q2+q3-q4)*(q1-q2-q3+q4)*(diff(diff(y(w), w), w))*y(w)+(3*q1+3*q2-3*q3-3*q4)*(diff(diff(y(w), w), w))*(diff(y(w), w))-3*(diff(diff(y(w), w), w))^2+(-q1-q2+q3+q4)*(diff(diff(diff(y(w), w), w), w))*y(w)+2*(diff(diff(diff(y(w), w), w), w))*(diff(y(w), w)) = 0

(1)

ans := dsolve(ode, y(w))

``

Download Ode_equation.mw

I am a newbie in the use of the Physics package.
As I'm interested in modeling dynamic articulated systems, I began reading the example about Mechanics (Statics).

My question is quite simple: let F some vector force of components a * _i and b * _j , what does abs(F) represent? 

I naively thought that abs(F)  was the modulus of F and expected it to be non negative. But I get some negative values (as in the tutorial example for some values of angle alpha.

Thanks in advance

How I can ontain results without Rootof !!

Thanks

help.mw

restart

EQ1 := c[11]*exp(-n*Pi*a/b)+c[12]*exp(n*Pi*a/b) = 0

c[11]*exp(-n*Pi*a/b)+c[12]*exp(n*Pi*a/b) = 0

(1)

EQ2 := c[11]*n*Pi/b-c[12]*n*Pi/b+b^2*Q[0, 1]*sin(n*Pi*y[0, 1]/b)*(n*Pi*exp(-n*Pi*x[0, 1]/b)/b+n*Pi*exp(n*Pi*x[0, 1]/b)/b)/(n*Pi) = c[21]*n*Pi/b-c[22]*n*Pi/b

c[11]*n*Pi/b-c[12]*n*Pi/b+b^2*Q[0, 1]*sin(n*Pi*y[0, 1]/b)*(n*Pi*exp(-n*Pi*x[0, 1]/b)/b+n*Pi*exp(n*Pi*x[0, 1]/b)/b)/(n*Pi) = c[21]*n*Pi/b-c[22]*n*Pi/b

(2)

c[21] := -b^2*Q[0, 2]*sin(n*Pi*y[0, 2]/b)*exp(-n*Pi*x[0, 2]/b)/(n*Pi)

-b^2*Q[0, 2]*sin(n*Pi*y[0, 2]/b)*exp(-n*Pi*x[0, 2]/b)/(n*Pi)

(3)

EQ3 := c[11]+c[12]+b^2*Q[0, 1]*sin(n*Pi*y[0, 1]/b)*(exp(-n*Pi*x[0, 1]/b)-exp(n*Pi*x[0, 1]/b))/(n*Pi) = lambda.(c[21]+c[22])

c[11]+c[12]+b^2*Q[0, 1]*sin(n*Pi*y[0, 1]/b)*(exp(-n*Pi*x[0, 1]/b)-exp(n*Pi*x[0, 1]/b))/(n*Pi) = lambda.(-b^2*Q[0, 2]*sin(n*Pi*y[0, 2]/b)*exp(-n*Pi*x[0, 2]/b)/(n*Pi)+c[22])

(4)

solve({EQ1, EQ2, EQ3}, {c[11], c[12], c[22]})

{c[11] = RootOf(exp(-n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]-exp(n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]-_Z*n*Pi*exp(-n*Pi*a/b)+_Z*n*Pi*exp(n*Pi*a/b)+(lambda.((exp(-n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+exp(n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+2*b^2*Q[0, 2]*sin(n*Pi*y[0, 2]/b)*exp(-n*Pi*x[0, 2]/b)*exp(n*Pi*a/b)+_Z*n*Pi*exp(-n*Pi*a/b)+_Z*n*Pi*exp(n*Pi*a/b))/(n*exp(n*Pi*a/b))))*n*exp(n*Pi*a/b)), c[12] = -RootOf(exp(-n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]-exp(n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]-_Z*n*Pi*exp(-n*Pi*a/b)+_Z*n*Pi*exp(n*Pi*a/b)+(lambda.((exp(-n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+exp(n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+2*b^2*Q[0, 2]*sin(n*Pi*y[0, 2]/b)*exp(-n*Pi*x[0, 2]/b)*exp(n*Pi*a/b)+_Z*n*Pi*exp(-n*Pi*a/b)+_Z*n*Pi*exp(n*Pi*a/b))/(n*exp(n*Pi*a/b))))*n*exp(n*Pi*a/b))*exp(-n*Pi*a/b)/exp(n*Pi*a/b), c[22] = -(exp(-n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+exp(n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+b^2*Q[0, 2]*sin(n*Pi*y[0, 2]/b)*exp(-n*Pi*x[0, 2]/b)*exp(n*Pi*a/b)+RootOf(exp(-n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]-exp(n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]-_Z*n*Pi*exp(-n*Pi*a/b)+_Z*n*Pi*exp(n*Pi*a/b)+(lambda.((exp(-n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+exp(n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+2*b^2*Q[0, 2]*sin(n*Pi*y[0, 2]/b)*exp(-n*Pi*x[0, 2]/b)*exp(n*Pi*a/b)+_Z*n*Pi*exp(-n*Pi*a/b)+_Z*n*Pi*exp(n*Pi*a/b))/(n*exp(n*Pi*a/b))))*n*exp(n*Pi*a/b))*Pi*n*exp(-n*Pi*a/b)+RootOf(exp(-n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]-exp(n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]-_Z*n*Pi*exp(-n*Pi*a/b)+_Z*n*Pi*exp(n*Pi*a/b)+(lambda.((exp(-n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+exp(n*Pi*x[0, 1]/b)*exp(n*Pi*a/b)*b^2*sin(n*Pi*y[0, 1]/b)*Q[0, 1]+2*b^2*Q[0, 2]*sin(n*Pi*y[0, 2]/b)*exp(-n*Pi*x[0, 2]/b)*exp(n*Pi*a/b)+_Z*n*Pi*exp(-n*Pi*a/b)+_Z*n*Pi*exp(n*Pi*a/b))/(n*exp(n*Pi*a/b))))*n*exp(n*Pi*a/b))*Pi*n*exp(n*Pi*a/b))/(Pi*n*exp(n*Pi*a/b))}

(5)

``

Download help.mw

problemfilepdsolve.mw
 

eq1 := diff(p(x, t), x)-p(x, t)*(1/(p(x, t)^2*q(x, t)^(1/3)))

diff(p(x, t), x)-1/(p(x, t)*q(x, t)^(1/3))

(1)

eq2 := diff(q(x, t), x)-(-3*q(x, t))*(1/(p(x, t)^2*q(x, t)^(1/3)))

diff(q(x, t), x)+3*q(x, t)^(2/3)/p(x, t)^2

(2)

pdsolve({eq1, eq2})

Error, (in pdsolve/sys) found the element '_F2' repeated in the indication of blocks variables

 

eq3 := diff(p(x), x)-p(x)*(1/(p(x)^2*q(x)^(1/3)))

diff(p(x), x)-1/(p(x)*q(x)^(1/3))

(3)

eq4 := diff(q(x), x)-(-3*q(x))*(1/(p(x)^2*q(x)^(1/3)))

diff(q(x), x)+3*q(x)^(2/3)/p(x)^2

(4)

dsolve({eq3, eq4})

[{q(x) = -27/(_C1*x+_C2)^3}, {p(x) = (-3*(diff(q(x), x))*q(x)^(2/3))^(1/2)/(diff(q(x), x)), p(x) = -(-3*(diff(q(x), x))*q(x)^(2/3))^(1/2)/(diff(q(x), x))}]

(5)

eq5 := diff(p(x, t), x)-x = 0

diff(p(x, t), x)-x = 0

(6)

pdsolve(eq5)

p(x, t) = (1/2)*x^2+_F1(t)

(7)

eq6 := diff(p(x), x)-x = 0

diff(p(x), x)-x = 0

(8)

dsolve(eq6)

p(x) = (1/2)*x^2+_C1

(9)

NULL

``

(10)


Help me in finding the solution of system eq1 and eq2.

Download problemfilepdsolve.mw

 

Maple 2020 beginner user - matrices shows 10 rows and columns on worksheet, by default. How to increase this value up to 16 and more? Of course, there is possibility (browse matrix) to see all values and export to Excel also, but better to see all 16 on worksheet. 

I would like to know which of the more than 100 worksheets I have in a Windows 11 folder execute the events operation within dsolve numeric.

Is there a way to identify which of this large number of Maple worksheets contain a given phrase e.g. "events"?

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