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Question: why odetest does not verify this same solution as Maple's but written different?

Question:why odetest does not verify this same solution as Maple's but written different?

nm 9889 Maple 2024
ode dsolve differential-equations odetest
August 23 2024
2

This is first order ode with IC. Solving it by Maple, then odetest verifies the Maple solution against the ode and the IC.

I solved it myself and got solution, which Maple says is same as its solution but my solution is written little different. Using simplify Maple says both solutions are same.

But I am not able to get zero when using odetest on my solution. No matter what I tried. I tried the tricks I know from before and from earlier questions/answers, but none of them worked on this one. So I have no idea what to try now.

It is clearly has something to do about how it is written. Even though it is  mathematically equivalent  to Maple's.

Would someone be able to find out why that is, and what trick is needed to make odetest verify my solution?

Since Maple says they are same, then odetest should give zero for my solution also.  odetest verifies my solution is correct only against the IC, but not against the ode itself. I did not show the output of odetest below since they are very very large.

Attached worksheet.

> 

restart;
> 

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 1792 and is the same as the version installed in this computer, created 2024, August 22, 12:6 hours Pacific Time.`

> 

libname;

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

> 

restart;
> 

ode:=3*x - y(x) + 1 + (x - 3*y(x) - 5)*diff(y(x), x) = 0;
IC:=y(0) = 0;

3*x-y(x)+1+(x-3*y(x)-5)*(diff(y(x), x)) = 0

y(0) = 0

> 

maple_sol:=dsolve([ode,IC],[dAlembert],implicit):
maple_sol:=simplify(%);
odetest(maple_sol,[ode,IC]);

3*(x+1)*((2/3)*((x+y(x)+3)/(-x+3*y(x)+5))^(2/3)*(x-3*y(x)-5)*((-4*x+4*y(x)+4)/(x-3*y(x)-5))^(1/3)+I*3^(1/6)*2^(2/3)+(1/3)*6^(2/3))/(((x+y(x)+3)/(-x+3*y(x)+5))^(2/3)*((-4*x+4*y(x)+4)/(x-3*y(x)-5))^(1/3)*(2*x-6*y(x)-10)) = 0

[0, 0]

> 

my_sol:=x + 2^(1/3)*(2^(2/3)*((y(x) + x + 3)/(-x + 3*y(x) + 5))^(2/3)*(x - 3*y(x) - 5)*((4*y(x) - 4*x + 4)/(x - 3*y(x) - 5))^(1/3) + 2^(2/3)*3^(2/3)*(-4)^(1/3)*(x + 1))/(((4*y(x) - 4*x + 4)/(x - 3*y(x) - 5))^(1/3)*((y(x) + x + 3)/(-x + 3*y(x) + 5))^(2/3)*(2*x - 6*y(x) - 10)) = 0;

x+2^(1/3)*(2^(2/3)*((x+y(x)+3)/(-x+3*y(x)+5))^(2/3)*(x-3*y(x)-5)*((-4*x+4*y(x)+4)/(x-3*y(x)-5))^(1/3)+2^(2/3)*3^(2/3)*(-4)^(1/3)*(x+1))/(((-4*x+4*y(x)+4)/(x-3*y(x)-5))^(1/3)*((x+y(x)+3)/(-x+3*y(x)+5))^(2/3)*(2*x-6*y(x)-10)) = 0

> 

#this shows my solution and Maple are same mathematically the same
simplify(lhs(maple_sol)-lhs(my_sol));

0

> 

simplify(maple_sol-my_sol);

0 = 0

> 

#but can't get odetest to give zero to my solution. Why?
the_residual:=odetest(my_sol,[ode,IC]):
evalb(the_residual=0);

false

> 

evalb(simplify(the_residual)=0);

false

> 

odetest(normal(my_sol),[ode,IC]): #did not work. Not zero. very long result

> 

odetest(radnormal(my_sol),[ode,IC]): #did not work. Not zero. very long result

> 

odetest(combine(my_sol),[ode,IC]): #did not work. Not zero. very long result

> 

odetest(evala(my_sol),[ode,IC]): #did not work. Not zero. very long result

> 

odetest(my_sol,[ode,IC]) assuming real: #did not work. Not zero. very long result

> 

odetest(my_sol,[ode,IC]) assuming x>0: #did not work. Not zero. very long result

> 

odetest(my_sol,[ode,IC]) assuming x<0: #did not work. Not zero. very long result

> 

odetest(expand(my_sol),[ode,IC]): #did not work. Not zero. very long result

> 

 


 

Download unable_to_get_odetest_to_verify_same_solution_august_23_2024.mw
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