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Question: Maple returns solution to ode with no solution?

Question:Maple returns solution to ode with no solution?

nm 9874 Maple 2024
ode dsolve differential-equations
September 10 2024
2

Why Maple returns y(x)=0 as solution to this ode when even odetest do not validate the solution? Solution satisfies the ode but not the given BC.

Is this a known bug?

I've updated the worksheet now to include few more examples, all using same ode but with different BC's. In all 4 examples, Maple gives solutions when there should not be solution and in one case gives solution which can not even be used for odetest. These are random BC's generated just for testing.
 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1804. The version installed in this computer is 1802 created 2024, September 3, 11:35 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

> 

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

> 

restart;
> 

#EXAMPLE 1
> 

ode:=diff(diff(y(x), x), x) + 2*diff(y(x), x)/x - y(x) = 0;
IC:=y(-1)=0,D(y)(-infinity)=-1/exp(1);

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

y(-1) = 0, (D(y))(-infinity) = -1/exp(1)

> 

maple_sol:=dsolve([ode,IC]);

y(x) = 0

> 

odetest(maple_sol,[ode,IC])

[0, 0, -exp(-1)]

> 

restart;

> 

#EXAMPLE 2
> 

ode:=diff(diff(y(x), x), x) + 2*diff(y(x), x)/x - y(x) = 0;
IC:=y(infinity)=0,D(y)(-infinity)=-1/exp(1);

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

y(infinity) = 0, (D(y))(-infinity) = -1/exp(1)

> 

maple_sol:=dsolve([ode,IC]);

y(x) = 0

> 

odetest(maple_sol,[ode,IC])

[0, 0, -exp(-1)]

> 

restart
> 

#EXAMPLE 3
> 

ode:=diff(diff(y(x), x), x) + 2*diff(y(x), x)/x - y(x) = 0;
IC:=y(-infinity)=0,D(y)(-infinity)=-1/exp(1);

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

y(-infinity) = 0, (D(y))(-infinity) = -1/exp(1)

> 

maple_sol:=dsolve([ode,IC]);

y(x) = signum((sinh(x)+cosh(x))/x)*infinity

> 

odetest(maple_sol,[ode,IC])

Error, (in signum) signum is not differentiable at 0

> 

#EXAMPLE  4
> 

restart;
> 

ode:=diff(diff(y(x), x), x) + 2*diff(y(x), x)/x - y(x) = 0;
IC:=y(-infinity)=0,D(y)(infinity)=-1/exp(1);

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

y(-infinity) = 0, (D(y))(infinity) = -1/exp(1)

> 

maple_sol:=dsolve([ode,IC]);

y(x) = 0

> 

odetest(maple_sol,[ode,IC])

[0, 0, -exp(-1)]

> 

 


 

Download wrong_sol_dsolve_sept_10_2024.mw

Update sept 13, 2024

Here is one more example I found. In this ode, the IC given leads to division by zero in the solution. Yet Maple for some reason removes the offending part of the solution with that constant, and returns the rest. 

Is one allowed to do this? odetest also do not validate the solution. There should not be solution returned in this case, since it is not possible to find values for the constants of integration given these initial conditions. Right?

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

restart;
> 

ode:=x^2*diff(y(x),x$2)+x*diff(y(x),x)-9*y(x)=0;
IC:=y(0)=1,D(y)(0)=0;
maple_sol_no_IC:=dsolve(ode);

x^2*(diff(diff(y(x), x), x))+x*(diff(y(x), x))-9*y(x) = 0

y(0) = 1, (D(y))(0) = 0

y(x) = c__1*x^3+c__2/x^3

> 

maple_sol_with_IC:=dsolve([ode,IC]); #maple just removed the c2/x^3 part. Since at x=0 gives problem?

y(x) = c__1*x^3

> 

odetest(maple_sol_with_IC,[ode,IC]); #shows solution does not verify

[0, 1, 0]

> 

 


 

Download another_example_solution_given_when_none_exist.mw

 

 
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