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Question: Why Maple says this ode is Bernoulli when it is not?

Question:Why Maple says this ode is Bernoulli when it is not?

nm 9934 Maple 2024
ode dsolve differential-equations bernoulli odeadvisor
September 15 2024
0

Bernoulli first order ode has form as show in wikipedia  and also on Maple own site as

Notice that it is P(x)*y above and not P(x)* y^(-1) so the y(x) must be linear in that term.   But when I give Maple this ode

ode:=diff(y(x),x) + x*y(x)^(-1)= y(x)^(-1);

Which is clearly not of the form above, it solves it as Bernoulli.  In the above ode, P(x) is x and Q(x) is 1 and n is -1.

The ode advisor correctly said it is separable. But trace shows it used Bernoulli. Also when asking it to solve it as Bernoulli, it does.

What Am I missing here?  Is it not wrong for Maple to use Bernoulli method on this ode which is not Bernoulli?

Worksheet below

> 

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 1805 and is the same as the version installed in this computer, created 2024, September 3, 11:35 hours Pacific Time.`

> 

libname;

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

> 

restart;
> 

ode:=diff(y(x),x) + x*y(x)^(-1)= y(x)^(-1);
IC:=y(1) = 0;
DEtools:-odeadvisor(ode);

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

y(1) = 0

[_separable]

> 

infolevel[dsolve]:=5;

5

> 

dsolve(ode,y(x));  #why this says it solved it as Bernoulli ?

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

<- Bernoulli successful

y(x) = (-x^2+c__1+2*x)^(1/2), y(x) = -(-x^2+c__1+2*x)^(1/2)

> 

dsolve(ode,y(x),[Bernoulli])

Classification methods on request

Methods to be used are: [Bernoulli]

----------------------------

* Tackling ODE using method: Bernoulli

--- Trying classification methods ---

trying Bernoulli

<- Bernoulli successful

y(x) = (-x^2+c__1+2*x)^(1/2), y(x) = -(-x^2+c__1+2*x)^(1/2)

 

 

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