BVP - nonlocal conditions

Questions
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1

Hello,

I’m just wondering about a possibility to solve following problem numerically.
Suppose we have a boundary value problem like y’‘(t) = f(y’(t),y(t)) defined on some real finite interval (a,b), with some quite “rare” conditions, something like
{y[0] = 0, Integrate[u,{t,a,b}]==0}.

Is there a function that can deal with conditions like that, or I just have to write something by my hand ?
Thanks

2

I’m not sure if I totally understand the additional equation with the integral. What is u in this?

Either way, no it’s not a typical kind of condition, so it’d require some thought about how to set up either as a simulation, a different equation, or as an entirely handwritten numerical method.