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Question: why is Maple not able to find solution to this first order ode? Only after adding implicit it can solve it

Question:why is Maple not able to find solution to this first order ode? Only after adding implicit it can solve it

nm 10184 Maple 2023
ode dsolve implicit explicit differential-equations
December 22 2023
1

This first order ode is quadrature with initial conditions. By existence theorem it has solution and is unique on some interval that includes the initial conditions (because f and f_y  are continuous on the initial condition).

But for some reason Maple can't find the solution, unless one adds 'implicit' option. Why is that? I thought that Maple will automatically return implicit solution if can't find explicit solution. 

So does one then needs to try with implicit solution again if no solution is returned? I am basically asking if this is expected behavior of dsolve.

Below is worksheet also with the solution that Maple verifies is valid and satisfies the ode and also initial conditions.

ode:=diff(y(x), x) = sin(y(x)) + 1;
ic:=y(0)=Pi;
sol:=dsolve([ode,ic]);

20212

> 

interface(version);

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

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1618 and is the same as the version installed in this computer, created 2023, November 29, 17:28 hours Pacific Time.`

> 

restart;

28544

> 

ode:=diff(y(x), x) = sin(y(x)) + 1;
ic:=y(0)=Pi;
sol:=dsolve([ode,ic]);

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

y(0) = Pi

> 

maple_sol:=dsolve([ode,ic],'implicit');
odetest(maple_sol,[ode,ic])

(2+x*tan((1/2)*y(x))+x)/(tan((1/2)*y(x))+1) = 0

[0, 0]

> 

maple_sol:=dsolve([ode,ic],y(x),'explicit');

> 

mysol:=y(x)=2*arccos(-x/(sqrt(4+4*x+2*x^2)));
odetest(mysol,[ode,ic]) assuming x>=0

y(x) = 2*Pi-2*arccos(x/(2*x^2+4*x+4)^(1/2))

[0, 0]

> 

 


 

Download unable_to_dsolve_quadature_dec_22_2023.mw

 
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