Wrong Answer in the sympy.dsolve for ode

[kang li]

[kang li]

On Friday, April 8, 2022 at 2:43:18 AM UTC+1 kang li wrote:

[Aaron Meurer]

It does look wrong, according to checkodesol(). Can you open an issue
in the SymPy issue tracker for this?

Aaron Meurer

On Thu, Apr 7, 2022 at 7:58 PM kang li <kang.mat...@gmail.com> wrote:
>
>
>
> On Friday, April 8, 2022 at 2:43:18 AM UTC+1 kang li wrote:
>>
>>

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[Oscar Benjamin]

It is wrong or at least useless since B(t) appears in the integral. A
correct and simple result is given by the 1st_linear hint:

In [111]: dsolve(expr, hint='1st_linear')
Out[111]:
⎛ ⌠ ⎞
⎜ ⎮ ⌠ ⎟ ⌠
⎜ ⎮ -⎮ a(t) dt ⎟ ⎮ a(t) dt
⎜ ⎮ ⌡ ⎟ ⌡
B(t) = ⎜C₁ - ⎮ ℯ dt⎟⋅ℯ
⎝ ⌡ ⎠

In [112]: sol = dsolve(expr, hint='1st_linear')

In [113]: checkodesol(expr, sol)
Out[113]: (True, 0)

The incorrect result comes from the 1st_exact solver. It's possible
that 1st_exact shouldn't match this or that there's a bug in the
1st_exact solver.

--
Oscar

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[emanuel.c...@gmail.com]

FWIW :

sage: var("t")
t
sage: B=function("B")
sage: a=function("a")
sage: de=B(t).diff(t)-a(t)*B(t)+1==0
sage: foo=desolve(de,B(t), ivar=t) ; foo
(_C - integrate(e^(-integrate(a(t), t)), t))*e^(integrate(a(t), t))

which checks :

sage: var("_C")
_C
sage: de.substitute_function(B,foo.function(t))
0 == 0

HTH,

​

[kang li]

Sure, here is the link to this issue. https://github.com/sympy/sympy/issues/23380