nm

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These are questions asked by nm

This looks like a bug I have not seen before. Any one seen this before?

Error, (in Handlers:-TrigExpOnly) cannot determine if this expression is true or false: tr_is_cos

Can others reproduce it? I am using Maple 2023.2 on windows 10

btw, I found that by doing int(evala(integrand),t) instead of int(integrand,t) then the error goes away but not all the time. Below are two examples. The first where evala() fixes it, but the second it does not fix it. 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1585 and is the same as the version installed in this computer, created 2023, October 29, 6:31 hours Pacific Time.`

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, October 25 2023 Build ID 1753458`

restart;

15332

integrand:=-(((sqrt(3)*sqrt(27983)*I + 276)*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3) + 15*I*sqrt(3)*sqrt(27983) + (25*(-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3))/2 + 2265)*(-150 + (-150 + (-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3))*sqrt(3)*I - (-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3) + 24*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3))*(150 + (-150 + (-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3))*sqrt(3)*I + (-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3) - 24*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3))*((sqrt(3)*sqrt(27983)*I + 276)*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3) - 15*I*sqrt(3)*sqrt(27983) - 2265)*exp(-t*((-594 + 6*I*sqrt(83949))^(2/3)/3 + (-594 + 6*I*sqrt(83949))^(1/3) + 50)/(-594 + 6*I*sqrt(83949))^(1/3))*(-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3)*((-594 + 6*I*sqrt(3)*sqrt(27983))^(2/3) + 12*(-594 + 6*I*sqrt(3)*sqrt(27983))^(1/3) + 150)*sin(t)*cos(t))/(10101630528*(sqrt(3)*sqrt(27983)*I - 99)^2*(sqrt(3)*sqrt(27983)*I + 27983/33)*exp(t)) - ((-594 + 6*I*sqrt(83949))^(2/3) + 12*(-594 + 6*I*sqrt(83949))^(1/3) + 150)*(2*I*sqrt(83949)*(-594 + 6*I*sqrt(83949))^(1/3) + 30*I*sqrt(83949) + 25*(-594 + 6*I*sqrt(83949))^(2/3) + 552*(-594 + 6*I*sqrt(83949))^(1/3) + 4530)*(-594 + 6*I*sqrt(83949))^(1/3)*(sqrt(83949)*(-594 + 6*I*sqrt(83949))^(1/3)*I - 15*I*sqrt(83949) + 276*(-594 + 6*I*sqrt(83949))^(1/3) - 2265)*exp(-t*((-594 + 6*I*sqrt(83949))^(2/3)/3 + (-594 + 6*I*sqrt(83949))^(1/3) + 50)/(-594 + 6*I*sqrt(83949))^(1/3))*(8*cos(t)^2/exp(t) - 4/exp(t))/(5196312*(sqrt(83949)*I + 27983/33)*(sqrt(83949)*I - 99)) + ((-594 + 6*I*sqrt(83949))^(2/3) + 12*(-594 + 6*I*sqrt(83949))^(1/3) + 150)*(2*I*sqrt(83949)*(-594 + 6*I*sqrt(83949))^(1/3) + 30*I*sqrt(83949) + 25*(-594 + 6*I*sqrt(83949))^(2/3) + 552*(-594 + 6*I*sqrt(83949))^(1/3) + 4530)*(-150 + (-594 + 6*I*sqrt(83949))^(2/3))*(-594 + 6*I*sqrt(83949))^(2/3)*exp(-t*((-594 + 6*I*sqrt(83949))^(2/3)/3 + (-594 + 6*I*sqrt(83949))^(1/3) + 50)/(-594 + 6*I*sqrt(83949))^(1/3))/(1154736*(sqrt(83949)*I + 27983/33)*(sqrt(83949)*I - 99)*exp(t)):

int(integrand,t)

Error, (in Handlers:-TrigExpOnly) cannot determine if this expression is true or false: tr_is_cos

 

Download handler_trig_exp_only_nov_18_2023.mw

But the trick of using evala() to avoid this error does not always work. Here is an example below. So need to find another workaround for this.

restart;

18704

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, October 25 2023 Build ID 1753458`

integrand2:=1/40406522112*I*(-594+6*I*3^(1/2)*27983^(1/2))^(2/3)*exp(t*(5/3*3^(1/2)*2^(1/2)
*sin(1/3*arctan(1/99*83949^(1/2))+1/6*Pi)-5*cos(1/3*arctan(1/99*83949^(1/2))+1/
6*Pi)*2^(1/2)-1))*(150+I*(-150+(-594+6*I*3^(1/2)*27983^(1/2))^(2/3))*3^(1/2)+(-\
594+6*I*3^(1/2)*27983^(1/2))^(2/3)-24*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3))*(
2265+(276+I*(27983^(1/2)+92)*3^(1/2)-27983^(1/2))*(-594+6*I*3^(1/2)*27983^(1/2)
)^(1/3)+5*I*(-151+3*27983^(1/2))*3^(1/2)+15*27983^(1/2))*(2265-25*(-594+6*I*3^(
1/2)*27983^(1/2))^(2/3)+(276+I*(-276+27983^(1/2))*3^(1/2)+3*27983^(1/2))*(-594+
6*I*3^(1/2)*27983^(1/2))^(1/3)+15*I*(151+27983^(1/2))*3^(1/2)-45*27983^(1/2))*(
(-594+6*I*3^(1/2)*27983^(1/2))^(2/3)+12*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3)+
150)*3^(1/2)*(-150+I*(-150+(-594+6*I*3^(1/2)*27983^(1/2))^(2/3))*3^(1/2)-(-594+
6*I*3^(1/2)*27983^(1/2))^(2/3)+24*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3))/(I*3^(1
/2)*27983^(1/2)+27983/33)/(I*3^(1/2)*27983^(1/2)-99)^2/exp(t)*sin(t)*cos(t)-1/
20785248*I*(I*(-594+6*I*3^(1/2)*27983^(1/2))^(2/3)*3^(1/2)+(-594+6*I*3^(1/2)*
27983^(1/2))^(2/3)-150*I*3^(1/2)-24*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3)+150)*
exp(5/3*3^(1/2)*sin(1/3*arctan(1/99*83949^(1/2))+1/6*Pi)*2^(1/2)*t-5*cos(1/3*
arctan(1/99*83949^(1/2))+1/6*Pi)*2^(1/2)*t-t)*(2265-25*(-594+6*I*3^(1/2)*27983^
(1/2))^(2/3)+(276+I*(-276+27983^(1/2))*3^(1/2)+3*27983^(1/2))*(-594+6*I*3^(1/2)
*27983^(1/2))^(1/3)+15*I*(151+27983^(1/2))*3^(1/2)-45*27983^(1/2))*(2265+(276+I
*(27983^(1/2)+92)*3^(1/2)-27983^(1/2))*(-594+6*I*3^(1/2)*27983^(1/2))^(1/3)+5*I
*(-151+3*27983^(1/2))*3^(1/2)+15*27983^(1/2))*(-594+6*I*3^(1/2)*27983^(1/2))^(1
/3)*3^(1/2)/(I*3^(1/2)*27983^(1/2)+27983/33)/(I*3^(1/2)*27983^(1/2)-99)*(8/exp(
t)*cos(t)^2-4/exp(t))+1/13856832*I*(-594+6*I*3^(1/2)*27983^(1/2))^(2/3)*(-450+I
*(-150+(-594+6*I*3^(1/2)*27983^(1/2))^(2/3))*3^(1/2)-3*(-594+6*I*3^(1/2)*27983^
(1/2))^(2/3))*exp(t*(5/3*3^(1/2)*2^(1/2)*sin(1/3*arctan(1/99*83949^(1/2))+1/6*
Pi)-5*cos(1/3*arctan(1/99*83949^(1/2))+1/6*Pi)*2^(1/2)-1))*(150+I*(-150+(-594+6
*I*3^(1/2)*27983^(1/2))^(2/3))*3^(1/2)+(-594+6*I*3^(1/2)*27983^(1/2))^(2/3)-24*
(-594+6*I*3^(1/2)*27983^(1/2))^(1/3))*(2265-25*(-594+6*I*3^(1/2)*27983^(1/2))^(
2/3)+(276+I*(-276+27983^(1/2))*3^(1/2)+3*27983^(1/2))*(-594+6*I*3^(1/2)*27983^(
1/2))^(1/3)+15*I*(151+27983^(1/2))*3^(1/2)-45*27983^(1/2))*3^(1/2)/(I*3^(1/2)*
27983^(1/2)+27983/33)/(I*3^(1/2)*27983^(1/2)-99)/exp(t):

int(integrand2,t);

Error, (in Handlers:-TrigExpOnly) cannot determine if this expression is true or false: tr_is_cos

int(evala(integrand2),t);

Error, (in Handlers:-TrigExpOnly) cannot determine if this expression is true or false: tr_is_cos

 

Download handler_trig_exp_version_2.mw

ps. send to Maplesoft support.

MmaTranslator:-Mma:-Chop  does not seem to work as advertised.. It is supposed to work like Mathematica's Chop, but it does not. Is this by design or is it a bug?

restart;

MmaTranslator:-Mma:-Chop(((1.378834798932344*10^(-15))*I)*t) ;

returns the same input (1.378834799*10^(-15))*I*t but

MmaTranslator:-Mma:-Chop(((1.378834798932344*10^(-15))*I));

now returns 0.

But compare to Mathematica:

This makes it not very useful to use if one has to remove all symbols from an expression first, Any workaround? Here is an actual example where I wanted to use it

ode:=[diff(x(t), t) = -3*x(t) + 4*y(t), diff(y(t), t) = 5*x(t) + 9*z(t), diff(z(t), t) = y(t) + 6*z(t)];
sol:=dsolve(ode):
evalf[16](sol);

gives

Gives

{x(t) = (0.8172764110864494 - (7.853170607134887*10^(-16))*I)*c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) - (1.150854759654687 + (3.398186702482929*10^(-16))*I)*c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + (0.3780227930126823 + (9.268277369231981*10^(-16))*I)*c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t), y(t) = c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) + c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t), z(t) = (-0.2435641206911610 + (1.431838044809606*10^(-16))*I)*c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) + (-0.08015596744746927 + (4.286632781083632*10^(-16))*I)*c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + (0.6323620634472722 - (5.261170533293161*10^(-16))*I)*c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t)}

But Chop does not work on this. 

Maple 2023.2

Would Any one be able to give some explanation as to why calling a proc, which does not change anything globally but only acts on the input given, returns different answer the second time it is called with the same exact input? I am not able to understand this result at all. 

Maple 2023.2 on windows 10.

restart;

27260

W:=Matrix(3, 3, [[x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)],[x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)/x],[x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)^2/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-3/4*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))^2/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)^2/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+3/4*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))^2/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)^2/x^2-x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2]]):
 

foo:=proc(W::Matrix,x::symbol)
   local W1:=W,W_det,W1_det;
   local F:=2*x^3-ln(x):

   W_det := LinearAlgebra:-Determinant(W);

   #change the first column
   W1[1..3,1] := Vector['column']([0,0,F/x^3]):

   W1_det := simplify(LinearAlgebra:-Determinant(W1)):

   simplify(W1_det/W_det);
end proc:
 

foo(W,x);

-x^(-(1/12)*((44+12*3^(1/2)*23^(1/2))^(2/3)+20*(44+12*3^(1/2)*23^(1/2))^(1/3)-20)/(44+12*3^(1/2)*23^(1/2))^(1/3))*(x^3-(1/2)*ln(x))*(3^(1/2)*((44+12*3^(1/2)*23^(1/2))^(2/3)+20)*cos((1/12)*3^(1/2)*((44+12*3^(1/2)*23^(1/2))^(2/3)+20)*ln(x)/(44+12*3^(1/2)*23^(1/2))^(1/3))+3*sin((1/12)*3^(1/2)*((44+12*3^(1/2)*23^(1/2))^(2/3)+20)*ln(x)/(44+12*3^(1/2)*23^(1/2))^(1/3))*((44+12*3^(1/2)*23^(1/2))^(2/3)-20))*3^(1/2)*(3^(1/2)*23^(1/2)+11/3)/((44+12*3^(1/2)*23^(1/2))^(1/3)*(11*3^(1/2)*23^(1/2)+207))

foo(W,x)

1

 

Download why_different_answer.mw

This is linear ode, third order, Euler type and inhomogeneous ode.

If I solve the homogeneous ode only, then ask Maple to give me a particular solution, then add these, I get much much smaller solution which Maple verifies is correct.

Now when asking Maple to solve the original inhomogeneous ode as is, the solution is much more complicated and much longer with unresolved integrals.

Why does not Maple give the simpler solution? Both are verified to be correct.

This is my theory: When asking maple to find only the particular solution, it seems to have used a different and advanced method to find yp. Which is new to me and trying to learn it. It is based on paper "D'Alembertian Solutions of Inhomogeneous Equations (differential, difference, and some other).

Undetermined coefficients method can't really be used on ode's such as this because its coefficients are not constant.

Now, when asking Maple to solve the inhomogeneous ode, it seems to have used variation of parameters method, which results in integrals, which can be hard to solve.

My question is: Why does not Maple give the same much shorter answer when asked to solve the ode as is? Should it not have done so? Any thoughts on why such large difference in answer? Why it did not use the same method to find yp when asked to solve the whole ode as that leads to much smaller and more elegant solution.

ps. debugging this, it uses LinearOperators:-dAsolver:-dAlembertianSolver which is called from ODEtools/particularsol/linear to find yp when calling DETools:-particularsol(ode); but for some reason, it does not do this when asking it to solve the whole ode directly (if it did, then one will expect same answer to result, right?)

Maple 2023.2 on windows 10.
 

restart;

189900

(1)

#the ode
ode:=x^3*diff(y(x), x, x, x) + x^2*diff(y(x), x, x) + 2*x*diff(y(x), x) - y(x) = 2*x^3 - ln(x);

x^3*(diff(diff(diff(y(x), x), x), x))+x^2*(diff(diff(y(x), x), x))+2*x*(diff(y(x), x))-y(x) = 2*x^3-ln(x)

(2)

# find y_h
yh:=dsolve(lhs(ode)=0);

y(x) = c__1*x^(-(1/6)*((44+12*69^(1/2))^(2/3)-4*(44+12*69^(1/2))^(1/3)-20)/(44+12*69^(1/2))^(1/3))+c__2*x^((1/12)*(-20+(44+12*69^(1/2))^(2/3)+8*(44+12*69^(1/2))^(1/3))/(44+12*69^(1/2))^(1/3))*sin((1/12)*(3^(1/2)*(44+12*69^(1/2))^(2/3)+20*3^(1/2))*ln(x)/(44+12*69^(1/2))^(1/3))+c__3*x^((1/12)*(-20+(44+12*69^(1/2))^(2/3)+8*(44+12*69^(1/2))^(1/3))/(44+12*69^(1/2))^(1/3))*cos((1/12)*(3^(1/2)*(44+12*69^(1/2))^(2/3)+20*3^(1/2))*ln(x)/(44+12*69^(1/2))^(1/3))

(3)

#find particular solution
yp:=DETools:-particularsol(ode);

y(x) = (2/17)*x^3+ln(x)+3

(4)

#test particular solution is correct
odetest(yp,ode);

0

(5)

#find general solution = yh+ yp
y_general:=y(x)=rhs(yh)+rhs(yp);

y(x) = c__1*x^(-(1/6)*((44+12*69^(1/2))^(2/3)-4*(44+12*69^(1/2))^(1/3)-20)/(44+12*69^(1/2))^(1/3))+c__2*x^((1/12)*(-20+(44+12*69^(1/2))^(2/3)+8*(44+12*69^(1/2))^(1/3))/(44+12*69^(1/2))^(1/3))*sin((1/12)*(3^(1/2)*(44+12*69^(1/2))^(2/3)+20*3^(1/2))*ln(x)/(44+12*69^(1/2))^(1/3))+c__3*x^((1/12)*(-20+(44+12*69^(1/2))^(2/3)+8*(44+12*69^(1/2))^(1/3))/(44+12*69^(1/2))^(1/3))*cos((1/12)*(3^(1/2)*(44+12*69^(1/2))^(2/3)+20*3^(1/2))*ln(x)/(44+12*69^(1/2))^(1/3))+(2/17)*x^3+ln(x)+3

(6)

#test general solution is correct
odetest(y_general,ode);

0

(7)

#now solve the ode directly using Maple. Why this solution is much more complicated?
y_general_direct_method:=dsolve(ode);

y(x) = -(Int(-(5/2)*(x^(-(1/400)*69^(1/2)*(44+12*69^(1/2))^(2/3)+(11/1200)*(44+12*69^(1/2))^(2/3)+(1/12)*(44+12*69^(1/2))^(1/3)+2/3))^2*(44+12*69^(1/2))^(1/3)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))^2+3*(44+12*69^(1/2))^(1/3)*69^(1/2)*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))^2-11*(44+12*69^(1/2))^(1/3)*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))^2-11*(44+12*69^(1/2))^(1/3)*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))^2+100*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))^2+100*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))^2)*(-2*x^3+ln(x))/(x^3*(3*3^(1/2)*23^(1/2)+11)*(11*3^(1/2)*23^(1/2)-207)), x))*x^((1/200)*69^(1/2)*(44+12*69^(1/2))^(2/3)-(11/600)*(44+12*69^(1/2))^(2/3)-(1/6)*(44+12*69^(1/2))^(1/3)+2/3)+(Int(-(5/6)*x^((1/200)*69^(1/2)*(44+12*69^(1/2))^(2/3)-(11/600)*(44+12*69^(1/2))^(2/3)-(1/6)*(44+12*69^(1/2))^(1/3)+2/3)*x^(-(1/400)*69^(1/2)*(44+12*69^(1/2))^(2/3)+(11/1200)*(44+12*69^(1/2))^(2/3)+(1/12)*(44+12*69^(1/2))^(1/3)+2/3)*(44+12*69^(1/2))^(1/3)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)*3^(1/2)*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))-9*(44+12*69^(1/2))^(1/3)*69^(1/2)*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))-11*(44+12*69^(1/2))^(1/3)*3^(1/2)*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))+33*(44+12*69^(1/2))^(1/3)*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))+100*3^(1/2)*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))+300*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x)))*(-2*x^3+ln(x))*3^(1/2)/(x^3*(3*3^(1/2)*23^(1/2)+11)*(11*3^(1/2)*23^(1/2)-207)), x))*x^(-(1/400)*69^(1/2)*(44+12*69^(1/2))^(2/3)+(11/1200)*(44+12*69^(1/2))^(2/3)+(1/12)*(44+12*69^(1/2))^(1/3)+2/3)*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))+(Int(-(5/6)*x^((1/200)*69^(1/2)*(44+12*69^(1/2))^(2/3)-(11/600)*(44+12*69^(1/2))^(2/3)-(1/6)*(44+12*69^(1/2))^(1/3)+2/3)*x^(-(1/400)*69^(1/2)*(44+12*69^(1/2))^(2/3)+(11/1200)*(44+12*69^(1/2))^(2/3)+(1/12)*(44+12*69^(1/2))^(1/3)+2/3)*(44+12*69^(1/2))^(1/3)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)*3^(1/2)*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))+9*(44+12*69^(1/2))^(1/3)*69^(1/2)*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))-11*(44+12*69^(1/2))^(1/3)*3^(1/2)*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))-33*(44+12*69^(1/2))^(1/3)*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))+100*3^(1/2)*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))-300*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x)))*(-2*x^3+ln(x))*3^(1/2)/(x^3*(3*3^(1/2)*23^(1/2)+11)*(11*3^(1/2)*23^(1/2)-207)), x))*x^(-(1/400)*69^(1/2)*(44+12*69^(1/2))^(2/3)+(11/1200)*(44+12*69^(1/2))^(2/3)+(1/12)*(44+12*69^(1/2))^(1/3)+2/3)*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))+c__1*x^((1/200)*69^(1/2)*(44+12*69^(1/2))^(2/3)-(11/600)*(44+12*69^(1/2))^(2/3)-(1/6)*(44+12*69^(1/2))^(1/3)+2/3)+c__2*x^(-(1/400)*69^(1/2)*(44+12*69^(1/2))^(2/3)+(11/1200)*(44+12*69^(1/2))^(2/3)+(1/12)*(44+12*69^(1/2))^(1/3)+2/3)*cos((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))+c__3*x^(-(1/400)*69^(1/2)*(44+12*69^(1/2))^(2/3)+(11/1200)*(44+12*69^(1/2))^(2/3)+(1/12)*(44+12*69^(1/2))^(1/3)+2/3)*sin((1/1200)*(44+12*69^(1/2))^(1/3)*3^(1/2)*(3*(44+12*69^(1/2))^(1/3)*69^(1/2)-11*(44+12*69^(1/2))^(1/3)+100)*ln(x))

(8)

#test the above
odetest(y_general_direct_method,ode);

0

(9)

 


 

Download why_such_difference_in_dsolve_answer.mw

THis came up in another maple forum.  Any one knows why

restart;
expr := -(r0+Delta_r)^2*(46*r0-41*Delta_r)*r0^5;
subsop(1=a,2=b,3=c,4=d, expr);

gives error Error, improper op or subscript selector

but changing the order works ok

subsop(4=d,3=c,2=b,1=a, expr);

               # a*b*c*d

Looked at help and nothing there I could see that would explain this. 

Maple 2023.2. 

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