This is second order ode solved using series method. This problem from textbook. The solution given by Maple does not match the book. I also solved this by hand and my hand solution agrees with the text book. I also solved this using Mathematica and its solution agrees with the book. 

Maple solution does not agree with the book for y2.  i.e. the general solution for this problem has the form 

    y= c_1 * y1 + c_2* (  y1 * ln(x)  +  y2 )

This is a Frobenius series method, since regular singular point and it falls into the hard case, where roots of indicial equation has difference of integer and where the second solution y2 can't be obtained using same method as y1 due to being undefined if using same method. So it require adjustment to the Frobenius series method.

This is ode

restart;
Order:=10;
ode:=x*diff(y(x),x$2)-3*diff(y(x),x)+x*y(x)=0;
dsolve(ode,y(x),'series')

Maple says that

   y2 = -144 - 36*x^2 + 1/2*x^6 - 25/1024*x^8 + ...)

First, it is missing x^4. And not able to make other coefficients match book. Book says y2 should be

   y2 = 1 + x^2/4 + x^4/64 - (11 x^6)/2304 + ....

And that is what I get and also Mathematica:

I do not have screen shot now of the page from the book to show. It is from an old textbook. Will try to make screen shot if needed.  This is problem 5, page 212 from SCHAUM's "differential equations" by Frank Ayers. 1952 edition. There is free PDF files on the net. Here is screen shot

My question is, why is Maple's series soluiton for the second basis solution y2 different? Could someone verify this? It also failes to verify it

restart;
ode:=x*diff(y(x),x$2)-3*diff(y(x),x)+x*y(x)=0;
Order:=10;
sol:=dsolve(ode,y(x),'series');
odetest(sol,ode,'series','point'=0)

Update

I've testsed few more problems, solved by hand and verified using Mathematica. All these problems give wrong solution by Maple for y_2. At least the solutions do not match the book and do not match my hand solution and do not match Mathematica. In all cases Mathematica's solution and my hand solution match the book. 

All these problem fall into the same difficult case of Frobenius series, where roots of indicial equation differ by integer and where y_2 can not be obtained directly using similar method used to obtain y_1. Other cases of Frobenius roots, Maple give complete correct general solutions. It is only this case where there seems to be something wrong.

In all of these problems below, y_1 solution is correct. It is the last series in y_2 shown which does not agree with book and it is this part which require using modifed method to obtain as explained on the book where these problems are solved from the above links. All the books used can be found online.

Please see attached worksheet.
 

Download series_solutions_Frob_difference_integer.mw

From https://maplesoft.zoom.us/webinar/register/WN_qidPG4qHRWGiTyO65vnGpw?timezone_id=Europe%2FParis

Is the recording of  Sneak Peek at Maple 2023 made on march 1,  available anywhere to see on Maple website or somewhere else? 

Update

Recording is at https://www.maplesoft.com/webinars/recorded/featured.aspx?id=2100  but need to first register/login if you are memeber of maplesoft.com

"The recording will start immediately after filling out the form."

What is the reason Maple likes to do this

arccos(sin(x));

         Pi/2 - arcsin(sin(x))

Both are correct, but the first has leaf count of only 3 and the second expression has leaf count of 11.

Surely the first is simpler to look at and read so the second form is not simpler.

What is the logic behind this automatic transformation? And did Maple always do this?

Found integration problem which causes server.exe to crash each time. I hope this can be used to help find why server.exe keeps crashing much more than before in Maple 2022.

This happens each time. The above is a typical example of what I have been saying all the time above server.exe crashing. It should not do that. If it can not solve the problem, it should simply return.

I hope these problems will be fixed in Maple 2023.

Any one can figure why it crashes?

Attached worksheet.

Download crash_feb_3_2023.mw

I am converting some code from Mathematica. In it there is this solution

eqs={2c2+c0==1,6c3+2c1==2,3c2+12c4==1};
FindInstance[eqs,{c0,c1,c2,c3,c4}]

Which gives

{{c0 -> 0, c1 -> 0, c2 -> 1/2, c3 -> 1/3, c4 -> -(1/24)}}

Maple's solve gives

eqs := [2*c2 + c0 = 1, 6*c3 + 2*c1 = 2, 3*c2 + 12*c4 = 1];
sol:=solve(eqs, {c0, c1, c2, c3, c4})

Gives

sol := {c0 = 1/3 + 8*c4, c1 = -3*c3 + 1, c2 = 1/3 - 4*c4, c3 = c3, c4 = c4}

I know that both are correct solutions. But I'am asking if there is a command or an option I overlooked that will generate the same result as the above from FindInstance, which will make it easier for me.

May be there is another solver package or command I could try?

I am not sure what algorithm FindInstance uses. The documentation page does not say.