nm

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13 years, 39 days

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These are questions asked by nm

 

In Maple 2020.2, and after I changed to interface(warnlevel=4); then once in a while, I now see this message 

                                  Warning, persistent store makes readlib obsolete

followed by name of the file and the line number. It always happen at calls to timelimit(the_time_limit,:-dsolve(....

It seems harmless so far, as I have not seen any side effect.

 

I googled and the above, and see few places where it shows up, but no clear explanation what it is and what it means. But the messages I saw at google are a little different. They look like this

               WARNING: persistent store makes one-argument readlib obsolete

While the one I get is a little different as you can see. (no one-argument in it)

I am using my own package in .mla file during running the code if this makes any difference.

Is there any place where it explains what this means and why it happens sometimes? Sorry, can't make MWE, since it seems to happen at random. But I noticed it always happens at call to dsolve when I saw it.

Maple 2020.2

Physics 884

Windows 10
 

This seems like a serious limitation of Maple module, unless I am missing something.

I am trying to refactor one of my module, putting some code in separate .mpl file, say B.mpl,  and then do, from the main module

   $include  "B.mpl"; 

 But Maple complain now that, since B.mpl has export in it, that I can't do that. 

But the code inside B.mpl works fine if I copy it back and paste it inside the module, in the same location where the $include  "B.mpl";  is

Here is an example. (Since I can't use $include  "B.mpl";  in worksheet, Maple does not like it, I replaced it in this example by read "B.mpl";

(btw, both the syntax  module A()   and A:=module() seem to be equivalent), the problem shows up with either form)

I also tried with ";" and witout ";" at the end of the $include , it still gives same error.

 

restart;

currentdir("....."); #set directory to where the folder is


module A()

read "B.mpl";

 export foo:=proc()
  0;
 end proc;
end module;

Where the file B.mpl is

export boo:=proc()
return 0;
end proc; 

How is one supposed to refactor long file to separate files if can't leave export on those proc's?  

If I put everything in one .mpl file, it works

module A()

#read "B.mpl";  

export boo:=proc()  #this proc was in B.mpl
return 0;
end proc; 

 export foo:=proc()
  0;
 end proc;
end module;

I did more testing, and found that this seems to be an issue in Maple 2020.2. Because I just tried the same thing in Maple 2019 and it worked there ! i.e. no error.

Any one knows what is going on? 

Maple 2020.2, Physics 884.   Windows 10.

Here is screen shot. Same code. Works OK in Maple 2019.2 but gives error in 2020.2

 

 

 

I'd like to define a proc, which takes first argument to be either an ode (i.e. type `=`) or set of ode's, or list of ode's.

However, I do not know how to tell Maple that the list or set, if that is the type, to be a list of `=` and no other type.

Here is what I tried to make it more clear

If I do this

restart;

interface(warnlevel=4);
kernelopts('assertlevel'=2): 


foo:=proc(ode::{`=`, set,list},func::`function`,$)
   print("ode=",ode);
   print("func=",func);
end proc:

Then Maple will check that the first argument is ANY one of `=`, set or list. 

But does not check if the list or set contains only equations of type `=`.  So I am able to call the above like this

ode1:=diff(y(x),x)=1:
ode2:=diff(y(x),x)=x:
foo(ode1,y(x));  #this is OK
foo([ode1,a],y(x))  #this is wrong

Which is wrong, since `a` is not of type `=`.

Next I tried this (I also wanted to check that if first argument is list or set, that it is not empty, so added extra check)

restart;
interface(warnlevel=4);
kernelopts('assertlevel'=2):

foo:=proc(ode::{`=`, 
                   And(set,satisfies(x-> (numelems(x)<>0 and type(x,`=`))  )),
                   And(list,satisfies(x-> (numelems(x)<>0 and type(x,`=`))  ))
                   },
                   func::`function`,$                                   
                   )

  print("ode=",ode);
  print("func=",func);
end proc;

But the above gives an error

ode1:=diff(y(x),x)=1:
ode2:=diff(y(x),x)=x:

foo([ode1,a],y(x))  

I also tried

foo:=proc(ode::{`=`, 
                   And(set,satisfies(x-> type(x,`=`)  )),
                   And(list,satisfies(x-> type(x,`=`) ))
                   },
                   func::`function`,$                                   
                   )

   print("ode=",ode);
   print("func=",func);

end proc;

Also gives erorr when called 

foo([ode1,ode2],y(x))

Ofcourse, I can just leave the check as in first case above, and in the proc itself, do the check myself manually by going over each entry in the list or set to make sure each entry is of type `=`. 

But I wanted Maple to do this work for me, if possible.

What is the correct syntax for doing so?

Maple 2020.2

 

why setting interface(warnlevel=0); makes dsolve change the form of the final solution to an ODE?

Is this to be expected? Help on warnlevel 0 says to just suppress all warnings

In this example, both solutions are equivalent. One is just simpler than the other.

But now I am worried if this setting could affect dsolve in other ways not yet anticipated.
 

restart;

interface(version);

`Standard Worksheet Interface, Maple 2020.2, Windows 10, November 11 2020 Build ID 1502365`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 884 and is the same as the version installed in this computer, created 2020, November 25, 16:49 hours Pacific Time.`

interface(warnlevel=0);

3

ic:=y(0)=3:
ode := diff(y(x),x)*y(x)/(1+1/2*sqrt(1+diff(y(x),x)^2))=-x:
sol_1:=dsolve([ode,ic],y(x),singsol=all);

y(x) = -3+(1/3)*(-9*x^2+324)^(1/2), y(x) = 1+(1/3)*(-9*x^2+36)^(1/2)

restart;

ic:=y(0)=3:
ode := diff(y(x),x)*y(x)/(1+1/2*sqrt(1+diff(y(x),x)^2))=-x:
sol_2:=dsolve([ode,ic],y(x),singsol=all);

y(x) = -3+(-x^2+36)^(1/2), y(x) = 1+(-x^2+4)^(1/2)


 

Download warnlevel_difference.mw

btw, the same thing happens with warnlevel 2. i.e. answers look different.

But with warnlevel 3 and 4, now dsolve gives the same answer. 

SInce it seems default is warnlevel 3, it seems internally, dsolve takes different path depending on warnlevel setting? 

Edit

Here is a movie. I am using windows 10.

 

Edit: Here is another video. Tried now with fresh start of Maple. i.e. closed Maple and started it again.  Using worksheet. No other worksheet was open. This is what I found. Initially it gives the longer solution. After couple of tries, it then changed to the simpler one

 

Hello Maple experts;

We've talked about this subject before. odetest not verifying dsolve output. And very useful input was given:

https://www.mapleprimes.com/questions/227546-How-To-Make-Odetest-Verify-Dsolve

https://www.mapleprimes.com/questions/227638-How-To-Make-Odetest-Give-Zero-On-Its

Here, I thought to give a collection from my ode database of ode's that are solved by Maple, but odetest does not give zero, all in one place. 

I know this is a hard problem to get odetest to always verify its own solution. May be each case needs custom solution?

It would be nice if this area in Maple could be improved on more if possible (Maple is already a CAS leader in solving ODE's).

If some of the experts here like to see if they can get odetest to give zero on some of these examples, they are welcome to and will be useful to see. I only tried just simplify().

I depend on odetest to tell me if my solution is correct or not, and getting false negative makes me spend more time trying to find where my error in my solution, where there might be no error there, and it is just that odetest could not verify it.

These are all from different text books. I put the reference on each ODE where it was obtained from.

Two of these ODE can also hang or take very long time. I indicated that there so one might want to skip these two.

edit added new one, #1822, uploaded new worksheet


 

interface(version);

`Standard Worksheet Interface, Maple 2020.2, Windows 10, November 11 2020 Build ID 1502365`

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 884 and is the same as the version installed in this computer, created 2020, November 25, 16:49 hours Pacific Time.`

#796
#Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
#Section: Section 1.2 Page 14
#Problem number: 9.
restart;
ode:=diff(y(x),x) = abs(y(x))+1;
sol:=dsolve(ode,y(x));
odetest(sol[1],ode):
simplify(%);

diff(y(x), x) = abs(y(x))+1

y(x) = -exp(-x)/_C1+1, y(x) = exp(x)*_C1-1

(-abs((-exp(-x)+_C1)/_C1)*_C1+exp(-x)-_C1)/_C1

#878
#Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
#Section: Section 2.3 Page 55
#Problem number: 10.
restart;
ode:=diff(y(x),x) = x*(y(x)^2-1)^(2/3);
sol:=dsolve(ode,y(x));
odetest(sol,ode):
simplify(%);

diff(y(x), x) = x*(y(x)^2-1)^(2/3)

(1/2)*x^2-(-signum(y(x)^2-1))^(2/3)*y(x)*hypergeom([1/2, 2/3], [3/2], y(x)^2)/signum(y(x)^2-1)^(2/3)+_C1 = 0

-x*(4*y(x)^2*(y(x)^2-1)^(2/3)*signum(y(x)^2-1)^(1/3)*hypergeom([3/2, 5/3], [5/2], y(x)^2)+9*(y(x)^2-1)^(2/3)*signum(y(x)^2-1)^(1/3)*hypergeom([1/2, 2/3], [3/2], y(x)^2)+9*(-signum(y(x)^2-1))^(1/3))

#903
#Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
#Section: Section 2.4 Page 57
#Problem number: 13.
restart;
ode:=diff(y(x),x)-y(x) = x*y(x)^(1/2);
ic:=y(0)=4;
sol:=dsolve([ode,ic],y(x));
odetest(sol,ode):
simplify(%);

diff(y(x), x)-y(x) = x*y(x)^(1/2)

y(0) = 4

y(x) = 16*(exp((1/2)*x))^2-8*x*exp((1/2)*x)+x^2-16*exp((1/2)*x)+4*x+4

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

#1330
#Book: Differential equations and their applications, 3rd ed., M. Braun
#Section: Section 1.10. Page 80
#Problem number: 5.
restart;
ode:=diff(y(t),t) = 1+y(t)+y(t)^2*cos(t);
sol:=dsolve(ode,y(t)):
timelimit(60,odetest(sol,ode)); #WARNING, will either hang or take long time then timeout

diff(y(t), t) = 1+y(t)+y(t)^2*cos(t)

#1498
#Book: Differential Gleichungen, Kamke, 3rd ed
#Section: section 1.0
#Problem number: 25.
restart;
ode:=diff(y(x),x) = c*x^(-1+v)+b*x^(2*v)-a*y(x)^2;
sol:=dsolve(ode,y(x)):
odetest(sol,ode): #output too long to post

diff(y(x), x) = c*x^(-1+v)+b*x^(2*v)-a*y(x)^2

#1822
#Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
#Section: Chapter 11.3, page 316
restart;
ode:=x*y(x)*diff(y(x),x) = (y(x)^2-9)^(1/2);
ic:=y(exp(4)) = 5;
sol:=dsolve([ode,ic],y(x));
odetest(sol,[ode,ic]);
#needs:
odetest(sol,[ode,ic]) assuming x>1

x*y(x)*(diff(y(x), x)) = (y(x)^2-9)^(1/2)

y(exp(4)) = 5

y(x) = (9+ln(x)^2)^(1/2)

[-ln(x)*(csgn(ln(x))-1), 0]

[0, 0]

#1966
#Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
#Section: Chapter 2
#Problem number: 92.
restart;
ode:=2*x*diff(y(x),x)-y(x) = ln(diff(y(x),x));
sol:=dsolve(ode,y(x));
odetest(sol[1],ode):
simplify(%);
odetest(sol[2],ode);
simplify(%);

2*x*(diff(y(x), x))-y(x) = ln(diff(y(x), x))

y(x) = 1+(4*_C1*x+1)^(1/2)-ln((1/2)*(1+(4*_C1*x+1)^(1/2))/x), y(x) = 1-(4*_C1*x+1)^(1/2)-ln(-(1/2)*(-1+(4*_C1*x+1)^(1/2))/x)

-ln(2)+ln((1+(4*_C1*x+1)^(1/2))/x)-ln((2*x*_C1+(4*_C1*x+1)^(1/2)+1)/(x*(1+(4*_C1*x+1)^(1/2))))

-ln(2)+ln(-(-1+(4*_C1*x+1)^(1/2))/x)-ln((-2*x*_C1+(4*_C1*x+1)^(1/2)-1)/(x*(-1+(4*_C1*x+1)^(1/2))))

-ln(2)+ln((-(4*_C1*x+1)^(1/2)+1)/x)-ln((-2*x*_C1+(4*_C1*x+1)^(1/2)-1)/(x*(-1+(4*_C1*x+1)^(1/2))))

#2031
#Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
#Section: Various 3
#Problem number: 57.
ode:=diff(y(x),x) = a*x^(n-1)+b*x^(2*n)+c*y(x)^2;
sol:=dsolve(ode,y(x)):
odetest(sol,ode):
simplify(%)

diff(y(x), x) = a*x^(n-1)+b*x^(2*n)+c*y(x)^2

(1/2)*(-20*(I*a*c*(n+6/5)*b^(3/2)+(1/5)*b*a*(2*x^(n+1)*b+a)*c^(3/2)+(6/5)*(n+4/3)*(I*b^(5/2)*x^(n+1)*c-b^2*c^(1/2)*(n+1)))*(n+1)*WhittakerW(-(I*c^(1/2)*a+(-2*n-2)*b^(1/2))/(b^(1/2)*(2*n+2)), 1/(2*n+2), (2*I)*b^(1/2)*c^(1/2)*x^(n+1)/(n+1))+WhittakerW(-I*c^(1/2)*a/(b^(1/2)*(2*n+2)), 1/(2*n+2), (2*I)*b^(1/2)*c^(1/2)*x^(n+1)/(n+1))*(-(7*I)*a*c*(n^2+(16/7)*n+8/7)*b^(3/2)-5*a^2*b*(n+6/5)*c^(3/2)+3*b^2*(2+n)*(n+4/3)*n*c^(1/2)+I*c^2*a^3*b^(1/2)))*_C1/(c^(3/2)*b^(3/2)*(I*c^(1/2)*a+(-3*n-4)*b^(1/2))*x^2*(WhittakerW(-I*c^(1/2)*a/(b^(1/2)*(2*n+2)), 1/(2*n+2), (2*I)*b^(1/2)*c^(1/2)*x^(n+1)/(n+1))*_C1+WhittakerM(-I*c^(1/2)*a/(b^(1/2)*(2*n+2)), 1/(2*n+2), (2*I)*b^(1/2)*c^(1/2)*x^(n+1)/(n+1))))

#2372
#Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
#Section: Various 14
#Problem number: 407
ode:=diff(y(x),x)*(x^3+1)^(2/3)+(1+y(x)^3)^(2/3) = 0;
sol:=dsolve(ode,y(x)):
odetest(sol,ode):
simplify(%)

(diff(y(x), x))*(x^3+1)^(2/3)+(1+y(x)^3)^(2/3) = 0

-9*((4/9)*(1+y(x)^3)^(2/3)*Pi*3^(1/2)*LegendreP(-1/3, -1/3, (-y(x)^3+1)/(1+y(x)^3))*(-x^3)^(1/6)+(-(4/9)*(1+y(x)^3)^(1/3)*Pi*3^(1/2)*(x^3+1)^(1/3)*LegendreP(-1/3, -1/3, (-x^3+1)/(x^3+1))+GAMMA(2/3)*(-x^3)^(1/6)*((-y(x)^6-y(x)^3)*hypergeom([4/3, 5/3], [7/3], -y(x)^3)+x^3*(1+y(x)^3)^(1/3)*hypergeom([4/3, 5/3], [7/3], -x^3)*(x^3+1)^(2/3)))*(-y(x)^3)^(1/6))/((-x^3)^(1/6)*(9*hypergeom([4/3, 5/3], [7/3], -y(x)^3)*y(x)^3*(-y(x)^3)^(1/6)*(1+y(x)^3)^(1/3)*GAMMA(2/3)-4*Pi*3^(1/2)*LegendreP(-1/3, -1/3, (-y(x)^3+1)/(1+y(x)^3))))

#3035
#Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
#Section: Various 37
#Problem number: 1118.
restart;
ode:=(diff(y(x),x)^2+1)^(1/2)+a*diff(y(x),x) = x;
sol:=[dsolve(ode,y(x))]:
odetest(sol[1],ode):
simplify(%);
odetest(sol[2],ode):
simplify(%)

((diff(y(x), x))^2+1)^(1/2)+a*(diff(y(x), x)) = x

((a^2+x^2-1)^(1/2)*(a^2-1)*((a^4+(x^2-1)*a^2+2*a*x*(a^2+x^2-1)^(1/2)+x^2)/(a^2-1)^2)^(1/2)+a^3+a*x^2+x*(a^2+x^2-1)^(1/2)-a)/((a^2+x^2-1)^(1/2)*(a^2-1))

-((-a^2+1)*(a^2+x^2-1)^(1/2)*((a^4+(x^2-1)*a^2-2*a*x*(a^2+x^2-1)^(1/2)+x^2)/(a^2-1)^2)^(1/2)+a^3+a*x^2-x*(a^2+x^2-1)^(1/2)-a)/((a^2+x^2-1)^(1/2)*(a^2-1))

#3036
#Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
#Section: Various 37
#Problem number: 1119.
restart;
ode:=(diff(y(x),x)^2+1)^(1/2)+a*diff(y(x),x) = y(x);
sol:=[dsolve(ode,y(x))];
odetest(sol[1],ode):
simplify(%);
odetest(sol[2],ode):
simplify(%)

((diff(y(x), x))^2+1)^(1/2)+a*(diff(y(x), x)) = y(x)

[x-Intat(-(a-1)*(a+1)/(-a*_a+(_a^2+a^2-1)^(1/2)), _a = y(x))-_C1 = 0, x-Intat((a-1)*(a+1)/(a*_a+(_a^2+a^2-1)^(1/2)), _a = y(x))-_C1 = 0]

(((y(x)^2*a^2+a^4-2*y(x)*(y(x)^2+a^2-1)^(1/2)*a+y(x)^2-a^2)/(a^2-1)^2)^(1/2)*a^2-(y(x)^2+a^2-1)^(1/2)*a+y(x)-((y(x)^2*a^2+a^4-2*y(x)*(y(x)^2+a^2-1)^(1/2)*a+y(x)^2-a^2)/(a^2-1)^2)^(1/2))/(a^2-1)

(((y(x)^2*a^2+a^4+2*y(x)*(y(x)^2+a^2-1)^(1/2)*a+y(x)^2-a^2)/(a^2-1)^2)^(1/2)*a^2+(y(x)^2+a^2-1)^(1/2)*a-((y(x)^2*a^2+a^4+2*y(x)*(y(x)^2+a^2-1)^(1/2)*a+y(x)^2-a^2)/(a^2-1)^2)^(1/2)+y(x))/(a^2-1)

#3040
#Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
#Section: Various 37
#Problem number: 1126.
restart;
ode:=a*x*(diff(y(x),x)^2+1)^(1/2)+x*diff(y(x),x)-y(x) = 0;
sol:=[dsolve(ode,y(x))];
odetest(sol[1],ode): #too large to display
odetest(sol[2],ode): #too large to display

a*x*((diff(y(x), x))^2+1)^(1/2)+x*(diff(y(x), x))-y(x) = 0

[x-exp(arcsinh(((-a^2*x^2+x^2+y(x)^2)^(1/2)*a+y(x))/((a^2-1)*x))/a)*_C1/((-a^2*x^2+a^2*y(x)^2+2*(-a^2*x^2+x^2+y(x)^2)^(1/2)*a*y(x)+x^2+y(x)^2)/((a^2-1)^2*x^2))^(1/2) = 0, x-exp(-arcsinh(((-a^2*x^2+x^2+y(x)^2)^(1/2)*a-y(x))/((a^2-1)*x))/a)*_C1/(-(a^2*x^2-a^2*y(x)^2+2*(-a^2*x^2+x^2+y(x)^2)^(1/2)*a*y(x)-x^2-y(x)^2)/((a^2-1)^2*x^2))^(1/2) = 0]

#3054
#Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
#Section: Various 37
#Problem number: 1146.
restart;
ode:=ln(diff(y(x),x))+4*x*diff(y(x),x)-2*y(x) = 0;
sol:=[dsolve(ode,y(x))];
odetest(sol[1],ode):
simplify(%);
odetest(sol[2],ode):
simplify(%);

ln(diff(y(x), x))+4*x*(diff(y(x), x))-2*y(x) = 0

[y(x) = (1/2)*ln((1/4)*(-1+(16*_C1*x+1)^(1/2))/x)-1/2+(1/2)*(16*_C1*x+1)^(1/2), y(x) = (1/2)*ln(-(1/4)*(1+(16*_C1*x+1)^(1/2))/x)-1/2-(1/2)*(16*_C1*x+1)^(1/2)]

ln(2)+ln((8*x*_C1-(16*_C1*x+1)^(1/2)+1)/(x*(-1+(16*_C1*x+1)^(1/2))))-ln((-1+(16*_C1*x+1)^(1/2))/x)

ln(2)+ln((-8*x*_C1-(16*_C1*x+1)^(1/2)-1)/(x*(1+(16*_C1*x+1)^(1/2))))-ln((-1-(16*_C1*x+1)^(1/2))/x)

#3128
#Book: Differential Equations, By George Boole F.R.S. 1865
#Section: Chapter 7
#Problem number: 7.
restart;
ode:=y(x) = a*diff(y(x),x)+(diff(y(x),x)^2+1)^(1/2);
sol:=[dsolve(ode,y(x))];
odetest(sol[1],ode):
simplify(%);
odetest(sol[2],ode):
simplify(%);

y(x) = a*(diff(y(x), x))+((diff(y(x), x))^2+1)^(1/2)

[x-Intat(-(a-1)*(a+1)/(-a*_a+(_a^2+a^2-1)^(1/2)), _a = y(x))-_C1 = 0, x-Intat((a-1)*(a+1)/(a*_a+(_a^2+a^2-1)^(1/2)), _a = y(x))-_C1 = 0]

((y(x)^2+a^2-1)^(1/2)*a-y(x)-((y(x)^2*a^2+a^4-2*y(x)*(y(x)^2+a^2-1)^(1/2)*a+y(x)^2-a^2)/(a^2-1)^2)^(1/2)*(a^2-1))/(a^2-1)

(-(y(x)^2+a^2-1)^(1/2)*a-y(x)-((y(x)^2*a^2+a^4+2*y(x)*(y(x)^2+a^2-1)^(1/2)*a+y(x)^2-a^2)/(a^2-1)^2)^(1/2)*(a^2-1))/(a^2-1)

#3129
#Book: Differential Equations, By George Boole F.R.S. 1865
#Section: Chapter 7
#Problem number: 8.
restart;
ode:=x = a*diff(y(x),x)+(diff(y(x),x)^2+1)^(1/2);
sol:=[dsolve(ode,y(x))];
odetest(sol[1],ode):
simplify(%);
odetest(sol[2],ode):
simplify(%);

x = a*(diff(y(x), x))+((diff(y(x), x))^2+1)^(1/2)

[y(x) = (1/2)*x*(a^2+x^2-1)^(1/2)/((a-1)*(a+1))+(1/2)*ln(x+(a^2+x^2-1)^(1/2))*a^2/((a-1)*(a+1))-(1/2)*ln(x+(a^2+x^2-1)^(1/2))/((a-1)*(a+1))+(1/2)*a*x^2/((a-1)*(a+1))+_C1, y(x) = -(1/2)*x*(a^2+x^2-1)^(1/2)/((a-1)*(a+1))-(1/2)*ln(x+(a^2+x^2-1)^(1/2))*a^2/((a-1)*(a+1))+(1/2)*ln(x+(a^2+x^2-1)^(1/2))/((a-1)*(a+1))+(1/2)*a*x^2/((a-1)*(a+1))+_C1]

-((a^2+x^2-1)^(1/2)*(a^2-1)*((2*a*x*(a^2+x^2-1)^(1/2)+a^4+(x^2-1)*a^2+x^2)/(a^2-1)^2)^(1/2)+a^3+a*x^2+x*(a^2+x^2-1)^(1/2)-a)/((a^2+x^2-1)^(1/2)*(a^2-1))

((-a^2+1)*(a^2+x^2-1)^(1/2)*((a^4+(x^2-1)*a^2-2*a*x*(a^2+x^2-1)^(1/2)+x^2)/(a^2-1)^2)^(1/2)+a^3+a*x^2-x*(a^2+x^2-1)^(1/2)-a)/((a^2+x^2-1)^(1/2)*(a^2-1))

#3136
#Book: Differential Equations, By George Boole F.R.S. 1865
#Section: Chapter 7
#Problem number: 15
restart;
ode:=y(x) =x*diff(y(x),x)+a*x*(diff(y(x),x)^2+1)^(1/2);
sol:=[dsolve(ode,y(x))];
odetest(sol[1],ode):
simplify(%):# output too large
odetest(sol[2],ode):
simplify(%):# output too large

y(x) = x*(diff(y(x), x))+a*x*((diff(y(x), x))^2+1)^(1/2)

[x-exp(arcsinh(((-a^2*x^2+x^2+y(x)^2)^(1/2)*a+y(x))/((a^2-1)*x))/a)*_C1/((-a^2*x^2+a^2*y(x)^2+2*(-a^2*x^2+x^2+y(x)^2)^(1/2)*a*y(x)+x^2+y(x)^2)/((a^2-1)^2*x^2))^(1/2) = 0, x-exp(-arcsinh(((-a^2*x^2+x^2+y(x)^2)^(1/2)*a-y(x))/((a^2-1)*x))/a)*_C1/(-(a^2*x^2-a^2*y(x)^2+2*(-a^2*x^2+x^2+y(x)^2)^(1/2)*a*y(x)-x^2-y(x)^2)/((a^2-1)^2*x^2))^(1/2) = 0]

#3138
#Book: Differential Equations, By George Boole F.R.S. 1865
#Section: Chapter 7
#Problem number: 17
restart;
ode:=x+y(x)*diff(y(x),x) = a*(diff(y(x),x)^2+1)^(1/2);
sol:=[dsolve(ode,y(x))];
odetest(sol[1],ode): #WARNING. hangs. try with timelimit

[y(x) = (a*(tan(RootOf(a^2*_Z^2*cos(2*_Z)+2*_C1*a*_Z*cos(2*_Z)+4*sin(_Z)*a*x*_Z-a^2*_Z^2+_C1^2*cos(2*_Z)+a^2*cos(2*_Z)+4*sin(_Z)*_C1*x-2*_C1*a*_Z-_C1^2+a^2-2*x^2))^2+1)^(1/2)-x)/tan(RootOf(a^2*_Z^2*cos(2*_Z)+2*_C1*a*_Z*cos(2*_Z)+4*sin(_Z)*a*x*_Z-a^2*_Z^2+_C1^2*cos(2*_Z)+a^2*cos(2*_Z)+4*sin(_Z)*_C1*x-2*_C1*a*_Z-_C1^2+a^2-2*x^2)), y(x) = (a*(tan(RootOf(a^2*_Z^2*cos(2*_Z)+2*_C1*a*_Z*cos(2*_Z)-4*sin(_Z)*a*x*_Z-a^2*_Z^2+_C1^2*cos(2*_Z)+a^2*cos(2*_Z)-4*sin(_Z)*_C1*x-2*_C1*a*_Z-_C1^2+a^2-2*x^2))^2+1)^(1/2)-x)/tan(RootOf(a^2*_Z^2*cos(2*_Z)+2*_C1*a*_Z*cos(2*_Z)-4*sin(_Z)*a*x*_Z-a^2*_Z^2+_C1^2*cos(2*_Z)+a^2*cos(2*_Z)-4*sin(_Z)*_C1*x-2*_C1*a*_Z-_C1^2+a^2-2*x^2))]

 


edit 12/23/2020

Found one more.

#3647
restart;
ode:=diff(y(x),x)=2*(x*sqrt(y(x))-1)*y(x);
ic:=y(0)=1;
sol:=dsolve([ode,ic]);
odetest(sol,ode);

The above becomes zero only for x>-1 

ps. I added this to the worksheet, but since upload now does not work, did not re upload so not to lose the display above. Will do that later when it is working.

 

edit 12/25/2020

Found one more.

#3607
#Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
#Section: Chapter 2, First order differential equations. Section 2.2 Exercises. page 46
#Problem number: 19.

restart;
ode:=1/2*diff(y(x),x) = (y(x)+1)^(1/2)*cos(x);
ic:=y(Pi)=0:
sol:=dsolve([ode,ic],y(x)):
res:=odetest(sol,ode);

edit 12/26/2020

Found one more

#3613
#Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
#Section: Chapter 2, First order differential equations. Section 2.2 Exercises. page 46
#Problem number: 26.

restart;
ode:=(x+1)*diff(y(x),x)+y(x)^(1/2) = 0;
ic:=y(0) = 1;
sol:=dsolve([ode,ic],y(x));
res:=odetest(sol,ode);

PDEtools:-Solve(res=0,x) assuming real;

edit 1/10/2021

Found one more

#2406
#Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
#Problem number: 406.

restart;
ode:=(x^3+1)^(2/3)*diff(y(x),x)+(y(x)^3+1)^(2/3) = 0;
sol:=dsolve(ode,y(x));

check:=simplify(odetest(sol,ode));  #tried other simplication, can't get it to zero. But sol is correct

 

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