boundary value problem

[Isaque Soares]

Does anyone knows how to solve a ode on sympy with this kind of bvp?

50𝑣(𝑥)+1000𝑑4𝑑𝑥4𝑣(𝑥)=−3

50𝑣(𝑥)+1000𝑑4𝑑𝑥4𝑣(𝑥)=−3

[Oscar Benjamin]

You can use dsolve for boundary value problems you just have to give the boundary conditions as the ICs argument e.g.:

In [27]: f = Function('f')                                                                                                                     

In [28]: t = Symbol('t')                                                                                                                    

In [29]: dsolve(f(t).diff(t, 2)-f(t))

Out[29]: 

           -t       t

f(t) = C₁⋅ℯ   + C₂⋅ℯ 

In [30]: dsolve(f(t).diff(t, 2)-f(t), ics={f(0):0, f(1):0})               

Out[30]: f(t) = 0

In [31]: dsolve(f(t).diff(t, 2)-f(t), ics={f(0):0, f(1):1})

Out[31]: 

            t          -t   

           ℯ          ℯ     

f(t) = ───────── - ─────────

       2⋅sinh(1)   2⋅sinh(1)

--

Oscar

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[Isaque Soares]

But how do I pass a constraint that is a function value that I don't know about yet to the ics dictionary? I mean the second constraint.

[Oscar Benjamin]

It doesn't look like dsolve can do that. I think it's worth opening an
issue on github for that.

To solve your problem right now you can set up the IC equations using
the general solution and solve for the constants with solve.

--
Oscar

On Mon, 27 Apr 2020 at 22:21, Isaque Soares <isaque...@gmail.com> wrote:
>
> But how do I pass a constraint that is a function value that I don't know about yet to the ics dictionary? I mean the second constraint.
>

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