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dharr

Dr. David Harrington

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21 years, 63 days
University of Victoria
Professor or university staff
Victoria, British Columbia, Canada

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Contact Dr. David Harrington
I am a retired professor of chemistry at the University of Victoria, BC, Canada. My research areas are electrochemistry and surface science. I have been a user of Maple since about 1990.

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These are answers submitted by dharr

Can't choose submethods...

dharr 8597
January 04 2024
2 2

It looks like you can choose homogeneous, but not subtypes of homogeneous, Abel but not subtypes of Abel, etc. It seems the subtypes are chosen automatically.

> 

restart;
> 

ode:=diff(y(x),x)*y(x)+a*x*y(x)+b*x^3=0;
DEtools:-odeadvisor(ode);

(diff(y(x), x))*y(x)+a*x*y(x)+b*x^3 = 0

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]

> 

sol:=dsolve(ode,[Abel]): #in list below; no error; gives solution
> 

sol:=dsolve(ode,[homogeneous_B]); #in list; no error; no solution

> 

infolevel[dsolve]:=5;

5

> 

sol:=dsolve(ode,[homogeneous]);

Classification methods on request

Methods to be used are: [homogeneous]

----------------------------

* Tackling ODE using method: homogeneous

--- Trying classification methods ---

trying homogeneous types:

trying homogeneous G

<- homogeneous successful

y(x) = RootOf(2*_Z^2-exp(RootOf(x^4*(tanh((1/2)*(a^2-8*b)^(1/2)*(-4*c__1+_Z+4*ln(x))/a)^2*a^2-8*tanh((1/2)*(a^2-8*b)^(1/2)*(-4*c__1+_Z+4*ln(x))/a)^2*b-a^2-8*exp(_Z)+8*b)))+b+_Z*a)*x^2

I'm guessing the choices have to be in this set, which would suggest you cannot limit it to homogeneous G - it probably looks at the symmetry and knows to use class G; similarly with Abel you do not get to choose 2nd type or class A

> 

`dsolve/keywords`;

{80, 81, `0F2`, `1F2`, `2F2`, `3F2`, Abel, Bessel, Bessel2, Chini, Euler, HINT, Heun, HeunB, HeunC, HeunD, HeunG, HeunT, Kovacic, Kummer, Lie, Mathieu, MeijerG, RIF, RNF, Riccati, Riemann, abaco1, abaco2, all, basis, can, can2, class, coeffs, con_sym, dif, diffalg, exact, exp_sym, fat, formal, fourier, gon, gon2, hyper3, ivars, k25, laplace, lin_sym, linear, missing, mu, mu_x_y1, mu_xy, mu_xy_2, mu_xyp, mu_xyp2, mu_y1, mu_y2, mu_y_y1, numeric, output, pFq, pdsolve, pot_sym, rifsimp, series, singsol, special, sym_1, sym_8, sym_pat, type, useInt, useint, way, Abel_AIL, Abel_AIR, Bernoulli, JacobiSN, Legendre, Liouville, `S-function`, WeierstrassP, Whittaker, Whittaker_old, arbitrary, coeff_type, const_coeffs, cylindrical, dAlembert, elliptic, exact_linear, exact_nonlinear, exp_reduce, explicit, formal_series, formal_solution, fouriercos, fouriersin, homogeneous, homogeneous_B, hypergeom, hypergeom1, hypergeom2, hypergeometric, implicit, inverse_Riccati, inverse_linear, linear_1, linear_patterns, linearizable, mhypergeom, mu_formal, mu_heuristic, mu_poly_yn, parametric, patterns, polynomial, quadrature, rational, reducible, separable, sym_implicit, to_Riccati, to_const_coeffs, DifferentialAlgebra, DifferentialThomas, Riccati_symmetries, WeierstrassPPrime, equivalent_to_Abel, equivalent_to_Bessel, fully_exact_linear, hypergeom_formal_sol, hypergeometricsols, `linear/missing_y`, linear_homogeneous, linear_nonhomogeneous, mhypergeom_formal_sol, mu_xyp_generalcase, mu_xyp_singularcases, nonlinear_homogeneous, rationalize_lode, special_functions, `sym_pat/[F(x)*G(y),0]`, `sym_pat/[F(x)+G(y),0]`, `sym_pat/[F(x),G(x)]`, `sym_pat/[F(x),G(y)]`, with_periodic_functions, exact_linear_nonhomogeneous, `linear_nonhomogeneous_[0,1]`, `linear_nonhomogeneous_[0,F(x)]`, linearizable_by_differentiation, `sym_pat/[F(x),G(x)*y+H(x)]`, mu_xyp2_dynamical_symmetries_fully_reducible, mu_xyp2_dynamical_symmetries_not_fully_reducible}

> 

NULL

Download dsolve.mw

cancel...

dharr 8597
January 02 2024
1 5

Here's one way. factor on a rational function is supposed to call normal, and normal is supposed to freeze appropriately, so this is surprisingly simple. (I just see your answer - I had asuumed you didn't want to move things to the other side.) I assume you want to cancel x from x^2+x and x^2 and not just the already factored ones. This also cancels common factors from numerator and denominator on each side.

> 

restart;
> 

cancel := proc(eq::`=`);
  local lhseq, rhseq, nums, dens;
  lhseq := factor(lhs(eq));
  rhseq := factor(rhs(eq));
  if lhseq = 0 or rhseq = 0 then return lhseq = rhseq end if;
  nums := factor(numer(lhseq)/numer(rhseq));
  dens := factor(denom(lhseq)/denom(rhseq));
  numer(nums)/numer(dens) = denom(nums)/denom(dens);
end proc:
> 

eq := (y-2*x)^3/((sin(y)-x)^2*(x^2+x)) = a/(x^2*(sin(y)-x)^3)

(y-2*x)^3/((sin(y)-x)^2*(x^2+x)) = a/(x^2*(sin(y)-x)^3)

> 

cancel(eq);

-(-y+2*x)^3/(x+1) = a/((sin(y)-x)*x)

> 

NULL

Download cancel.mw

Missing parameter values...

dharr 8597
December 31 2023
1 1

Correction to your Error.mw worksheet.
Two parameters didn't have values - one because the subscript f got automatically changed to f(x); the other was a typo. For efficiency reasons do not increase Digits. At the default Digits, the equations will be solved at hardware precision, if you ask for higher Digits (typically above 15), you use much slower routines. Changes in red.

Error.mw

missing parameter values...

dharr 8597
December 30 2023
0 0

Two parameters didn't have values - one because the subscript f got automatically changed to f(x); the other was a typo. For efficiency reasons do not increase Digits. At the default Digits, the equations will be solved at hardware precision, if you ask for higher Digits (typically above 15), you use much slower routines. Changes in red.

Error.mw

version...

dharr 8597
December 30 2023
2 0

You didn't say which version, but in 2023.2.1 it gives the trig form directly. The exp form can be converted using convert(...,trig)

> 

restart
> 

interface(version)

`Standard Worksheet Interface, Maple 2023.2, Windows 10, November 24 2023 Build ID 1762575`

> 

z := int(x^17*cos(x^6), x)

(1/3)*x^6*cos(x^6)+(1/6)*(x^12-2)*sin(x^6)

> 

z2 := collect(convert(z, exp), exp)

((1/6)*x^6+((1/12)*I)*(x^12-2))*exp(-I*x^6)+((1/6)*x^6-((1/12)*I)*(x^12-2))*exp(I*x^6)

> 

simplify(convert(z2, trig))

(1/3)*x^6*cos(x^6)+(1/6)*sin(x^6)*x^12-(1/3)*sin(x^6)

> 

NULL

Download int.mw

Shorter answer...

dharr 8597
December 28 2023
2 9

This is an answer to the newer, now deleted, question about how to make the subsindets transformer into a one-line procedure.

I think this does what you want. Unfortunately this code only works in 1-D.

subsindets(ex,specfunc(Units:-Unit),q->local un:=indets(q,name);eval(op(q),un=~map(Units:-Unit,un)));

Slightly longer version that works in  2-D is 

subsindets(ex,specfunc(Units:-Unit),proc(q) local un:=indets(q,name); eval(op(q),un=~map(Units:-Unit,un)) end)

Expansion_of_compound_units_shorter.mw

shorter...

dharr 8597
December 28 2023
0 0

I think this does what you want. Unfortunately this code only works in 1-D.

subsindets(ex,specfunc(Units:-Unit),q->local un:=indets(q,name);eval(op(q),un=~map(Units:-Unit,un)));

Slightly longer version that works in  2-D is 

subsindets(ex,specfunc(Units:-Unit),proc(q) local un:=indets(q,name); eval(op(q),un=~map(Units:-Unit,un)) end)

Expansion_of_compound_units_shorter.mw

not unusual...

dharr 8597
December 28 2023
2 1

It is not unusual for solutions to be independent of some parameters. Here's a simple example

eq1:=(x-a)*(y-b);
eq2:=x^2-b^2;
solve({eq1,eq2},{x,y});

gives

series solution...

dharr 8597
December 24 2023
1 0

It's not very clear what you want. However you do it, you need dsolve to solve an ODE. In this case there seems to be an exact solution, which you can then write in series form, if that is the objective.

> 

restart
> 

params := {H = 0, Nc = .2, Sh = .5, alpha = (1/2)*Pi, `&epsilon;` = .4, R[d] = .7}
> 

G := (1+4*R[d])*(diff(g(x), `$`(x, 2)))-Sh*sin(alpha)*g(x)^2-(Nc*(1-`&epsilon;`)+Nc+H)*g(x)

(1+4*R[d])*(diff(diff(g(x), x), x))-Sh*sin(alpha)*g(x)^2-(Nc*(1-epsilon)+Nc+H)*g(x)

> 

BCS := g(1) = 1, (D(g))(0) = 0

g(1) = 1, (D(g))(0) = 0

> 

ans := dsolve(eval({BCS, G}, params), g(x))

g(x) = (24/25)*tanh((1/95)*190^(1/2)*x)^2-24/25

> 

series(rhs(ans), x, 5)

series(-24/25+(48/2375)*x^2-(64/225625)*x^4+O(x^6),x,6)

> 

NULL

Download AGM.mw

LinearAlgebra...

dharr 8597
December 21 2023
3 1

You were using the old linalg package commands on the newer Matrix (not matrix) objects. I updated to the LinearAlgebra package with the newer commands.

maps.mw

Bug reporting...

dharr 8597
December 21 2023
0 0

That's quite dramatic! No chugging away for a longtime before losing the kernel as more usually happens. To submit a bug report log in to Mapleprimes, choose the "more" menu, then Submit software change request. In the form there is somewhere to enter additional information, and I often enter the mapleprimes link there (which I copy before I start the form).

Some are there...

dharr 8597
December 17 2023
3 1

The four Appell functions are there, and related functions such as the four Theta functions (JacobiTheta1, etc). For working with q-series and related stuff like Rogers-Ramanujan, see also Frank Garvin's (old-style) Maple packages here. 

> 

restart;
> 

FunctionAdvisor(function_classes);

[trig, trigh, arctrig, arctrigh, elementary, GAMMA_related, Psi_related, Kelvin, Airy, Hankel, Bessel_related, `0F1`, orthogonal_polynomials, Ei_related, erf_related, Kummer, Whittaker, Cylinder, `1F1`, Elliptic_related, Legendre, Chebyshev, `2F1`, Lommel, Struve_related, hypergeometric, Jacobi_related, InverseJacobi_related, Elliptic_doubly_periodic, Weierstrass_related, Zeta_related, complex_components, piecewise_related, Other, Bell, Heun, Appell, trigall, arctrigall, Polylog_related, integral_transforms]

> 

FunctionAdvisor(Appell);

The 4 functions in the "Appell" class are:

[AppellF1, AppellF2, AppellF3, AppellF4]

> 

FunctionAdvisor(definition,AppellF4);

[AppellF4(a, b, c__1, c__2, z__1, z__2) = Sum(Sum(pochhammer(a, _k1+_k2)*pochhammer(b, _k1+_k2)*z__1^_k1*z__2^_k2/(pochhammer(c__1, _k1)*pochhammer(c__2, _k2)*factorial(_k1)*factorial(_k2)), _k2 = 0 .. infinity), _k1 = 0 .. infinity), abs(z__1)^(1/2)+abs(z__2)^(1/2) < 1]

> 

FunctionAdvisor(Jacobi_related);

The 18 functions in the "Jacobi_related" class are:

[JacobiAM, JacobiCD, JacobiCN, JacobiCS, JacobiDC, JacobiDN, JacobiDS, JacobiNC, JacobiND, JacobiNS, JacobiSC, JacobiSD, JacobiSN, JacobiTheta1, JacobiTheta2, JacobiTheta3, JacobiTheta4, JacobiZeta]

> 

FunctionAdvisor(definition,JacobiTheta1);

[JacobiTheta1(z, q) = Sum(2*q^((_k1+1/2)^2)*sin(z*(2*_k1+1))*(-1)^_k1, _k1 = 0 .. infinity), abs(q) < 1]

> 

NULL

Download qFunctions.mw

eta vs Nr...

dharr 8597
December 17 2023
1 0

It's not clear what you want to plot. I'm guessing eta vs Nr for Nr=0.1, 0.3, 0.6, (for x=0) so there are only 3 points on this plot?

FE-2.mw

 

Inconsistent system...

dharr 8597
December 17 2023
3 1

Since your equations are linear, I converted them to Matrix form, then LinearSolve reports that the system is inconsistent. Note that the determinant of your matrix is zero and the rank is only 12. (I assume that eq[16] being the only one with a constant term is correct - but is the constant correct?) So there are relationships between the equations, and perhaps between the original differential equations. Using Nullspace to see what the relationships are between columns of the Matrix doesn't show anything obvious.

Perhaps Maple can solve the system of equations symbolically so it is easier to see what the relationships might be. Or you could set up the differential equations in Matrix form to make it more obvious what is happening.

Timoshenko_Beam.mw

another way for display only...

dharr 8597
December 16 2023
2 0

This prints in the same typeface as usual.

> 

restart

Setup so pp(expr) prettyprints expr with "," as decimal separator

> 

pp:=(expr)->Typesetting:-Typeset(expr):
`print/mn`:=x->Typesetting:-mn(StringTools:-Subs("."=",",x)):
> 

q := 1.23+sqrt((1.5+y)/sqrt(sin(1.45)+3.5*x))
pp(%)

Parse:-ConvertTo1D, "invalid input %1", Typesetting:-mprintslash([Typesetting:-mrow(Typesetting:-mn("1,23"), Typesetting:-mo("&plus;"), Typesetting:-msqrt(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("1,5"), Typesetting:-mo("&plus;"), Typesetting:-mi("y")), Typesetting:-msqrt(Typesetting:-mrow(Typesetting:-mn("0,9927129910"), Typesetting:-mo("&plus;"), Typesetting:-mrow(Typesetting:-mn("3,5"), Typesetting:-mo("&InvisibleTimes;"), Typesetting:-mi("x")))))))], [Typesetting:-mrow(Typesetting:-mn("1.23"), Typesetting:-mo("&plus;"), Typesetting:-msqrt(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("1.5"), Typesetting:-mo("&plus;"), Typesetting:-mi("y")), Typesetting:-msqrt(Typesetting:-mrow(Typesetting:-mn("0.9927129910"), Typesetting:-mo("&plus;"), Typesetting:-mrow(Typesetting:-mn("3.5"), Typesetting:-mo("&InvisibleTimes;"), Typesetting:-mi("x")))))))])

> 

NULL

Download comma.mw

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