Question: why dsolve with Lie option gives ones less solution in Maple 2024?

The ode  diff(y(x), x)^3 = y(x)*sin(x) should have 3 solutions since it is cubic in diff(y(x),x) and the each of the 3 generated ode's has one solution.

ode:=diff(y(x), x)^3 = y(x)*sin(x);
sol:=PDEtools:-Solve(ode,diff(y(x),x));
Vector(map(X->dsolve(X,'explicit'),[sol]))

But In Maple 2024, using Lie option gives 2 solutions only, while default dsolve gives 3 solutions.

In Maple 2023 using Lie option gives 6 solutions for some reason.

So something changed in Lie solver for dsolve.

Btw, in all the above I am discarding the extra y=0 solution as this is trivial solution and should not have been returned any way, but this is not a big issue

Basically, Maple 2024 Lie solver gives now 2 non trivial solutions when there should be 3 non trivial solutions.

Any one could give an idea why this happens? Should not both solvers return same number of non trivial solutions?


 

18364

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1711. The version installed in this computer is 1708 created 2024, March 27, 16:20 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

ode:=diff(y(x), x)^3 = y(x)*sin(x)

(diff(y(x), x))^3 = y(x)*sin(x)

Vector([dsolve(ode)])

Vector(4, {(1) = y(x) = 0, (2) = (3/2)*y(x)^(2/3)+Intat(-(y(x)*sin(_a))^(1/3)/y(x)^(1/3), _a = x)+_C1 = 0, (3) = (3/2)*y(x)^(2/3)+Intat((1/2)*(y(x)*sin(_a))^(1/3)*(1+I*sqrt(3))/y(x)^(1/3), _a = x)+_C1 = 0, (4) = (3/2)*y(x)^(2/3)+Intat(-(1/2)*(y(x)*sin(_a))^(1/3)*(I*sqrt(3)-1)/y(x)^(1/3), _a = x)+_C1 = 0})

Vector([dsolve(ode,useInt,'explicit')])

Vector(4, {(1) = y(x) = 0, (2) = y(x) = RootOf(3*_Z^(2/3)+2*(Int(-(_Z*sin(_a))^(1/3)/_Z^(1/3), _a = _b .. x))+2*_C1), (3) = y(x) = RootOf(3*_Z^(2/3)+2*(Int((1/2)*(_Z*sin(_a))^(1/3)*(1+I*sqrt(3))/_Z^(1/3), _a = _b .. x))+2*_C1), (4) = y(x) = RootOf(3*_Z^(2/3)+2*(Int(-(1/2)*(_Z*sin(_a))^(1/3)*(I*sqrt(3)-1)/_Z^(1/3), _a = _b .. x))+2*_C1)})

Vector([dsolve(ode,Lie)])

Vector(3, {(1) = y(x) = 0, (2) = y(x) = -(2/9)*(_C1+Int(exp((1/3)*(Int(cot(x), x))), x))*sqrt(6)*sqrt(exp((1/3)*(Int(cot(x), x)))*sin(x)*(_C1+Int(exp((1/3)*(Int(cot(x), x))), x)))/(exp((1/3)*(Int(cot(x), x))))^2, (3) = y(x) = (2/9)*(_C1+Int(exp((1/3)*(Int(cot(x), x))), x))*sqrt(6)*sqrt(exp((1/3)*(Int(cot(x), x)))*sin(x)*(_C1+Int(exp((1/3)*(Int(cot(x), x))), x)))/(exp((1/3)*(Int(cot(x), x))))^2})

 


 

Download why_one_less_solution_from_Lie.mw

This below is in Maple 2023 showing difference in Lie solutions
 


 

21112

interface(version);

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

ode:=diff(y(x), x)^3 = y(x)*sin(x)

(diff(y(x), x))^3 = y(x)*sin(x)

Vector([dsolve(ode)]);

Vector(4, {(1) = y(x) = 0, (2) = (3/2)*y(x)^(2/3)+Intat(-(y(x)*sin(_a))^(1/3)/y(x)^(1/3), _a = x)+_C1 = 0, (3) = (3/2)*y(x)^(2/3)+Intat((1/2)*(y(x)*sin(_a))^(1/3)*(1+I*sqrt(3))/y(x)^(1/3), _a = x)+_C1 = 0, (4) = (3/2)*y(x)^(2/3)+Intat(-(1/2)*(y(x)*sin(_a))^(1/3)*(I*sqrt(3)-1)/y(x)^(1/3), _a = x)+_C1 = 0})

Vector([dsolve(ode,Lie)])

Vector(7, {(1) = y(x) = 0, (2) = y(x) = -(2/9)*(_C1+Int(sin(x)^(1/3), x))*sqrt(6*sin(x)^(2/3)*(Int(sin(x)^(1/3), x))+6*sin(x)^(2/3)*_C1)/sin(x)^(1/3), (3) = y(x) = (2/9)*(_C1+Int(sin(x)^(1/3), x))*sqrt(6*sin(x)^(2/3)*(Int(sin(x)^(1/3), x))+6*sin(x)^(2/3)*_C1)/sin(x)^(1/3), (4) = y(x) = -(1/9)*((2*I)*_C1-I*(Int(sin(x)^(1/3), x))+sqrt(3)*(Int(sin(x)^(1/3), x)))*sqrt(3)*sqrt(I*sin(x)^(2/3)*((2*I)*_C1-I*(Int(sin(x)^(1/3), x))+sqrt(3)*(Int(sin(x)^(1/3), x))))/sin(x)^(1/3), (5) = y(x) = (1/9)*((2*I)*_C1-I*(Int(sin(x)^(1/3), x))+sqrt(3)*(Int(sin(x)^(1/3), x)))*sqrt(3)*sqrt(I*sin(x)^(2/3)*((2*I)*_C1-I*(Int(sin(x)^(1/3), x))+sqrt(3)*(Int(sin(x)^(1/3), x))))/sin(x)^(1/3), (6) = y(x) = -(1/9)*(sqrt(3)*(Int(sin(x)^(1/3), x))-(2*I)*_C1+I*(Int(sin(x)^(1/3), x)))*sqrt(3)*sqrt(-I*sin(x)^(2/3)*(sqrt(3)*(Int(sin(x)^(1/3), x))-(2*I)*_C1+I*(Int(sin(x)^(1/3), x))))/sin(x)^(1/3), (7) = y(x) = (1/9)*(sqrt(3)*(Int(sin(x)^(1/3), x))-(2*I)*_C1+I*(Int(sin(x)^(1/3), x)))*sqrt(3)*sqrt(-I*sin(x)^(2/3)*(sqrt(3)*(Int(sin(x)^(1/3), x))-(2*I)*_C1+I*(Int(sin(x)^(1/3), x))))/sin(x)^(1/3)})

 


 

Download Lie_solution_maple_2023.mw

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