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Question: why the way solution is written affects odetest result?

Question:why the way solution is written affects odetest result?

nm 8552 Maple 2020
ode differential-equations odetest
October 18 2020
2

I found a new strange thing with odetest that I have not seen before.

Would you say that these two solutions are the same or not?

They look the same to me.  One just have all the terms on one side, that is all.

Why would Maple odetest verify the first one but not the second? I did not know that all terms have to be on one side before. Is this documented somewhere?

Please see worksheet below.

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2020.1, Windows 10, July 30 2020 Build ID 1482634`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 847 and is the same as the version installed in this computer, created 2020, October 17, 17:3 hours Pacific Time.`

> 

ode:=diff(y(x), x) - 2*y(x) = 2*sqrt(y(x));
ic:=[y(0)=1];
maple_sol:=dsolve([ode,op(ic)],implicit);
odetest(maple_sol,[ode,op(ic)]) assuming x>0

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

[y(0) = 1]

1-2*exp(x)+y(x)^(1/2) = 0

[0, 0]

> 

#now move some terms to one side, and odetest no longer verifies it
my_sol:=y(x)^(1/2) = -1+2*exp(x);
odetest(my_sol,[ode,op(ic)]) assuming x>0

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

[diff(y(x), x)-2*y(x)+2-4*exp(x), 0]

> 

#the solution is to put all terms on one side
my_sol:=y(x)^(1/2) = -1+2*exp(x);
odetest(rhs(my_sol)-lhs(my_sol)=0,[ode,op(ic)]) assuming x>0

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

[0, 0]

> 

 


 

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