At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
No. "Initial conditions" is an arbitrary marker. So is t=0.
boundary is when they give t=a, t=b. rather than y(a)=k1 , y'(a)= k2 and so on.
If those are the only boundaries they give you, I can't tell you anything about "initial conditions". I would guess that they mean for t=a to be the initial condition, but it's not necessarily 0 unless there's other information.
There's not really enough info for me to understand what you're doing, but it looks to me like you have boundary values, not initial values.
Show that the problem y'=2x, y(0)=0, y(1)=100, has no solution. Is this an initial value problem?
It looks like a boundary value problem, but I don't think it really is. It just demonstrates that the two initial values contradict\[y'=2x\]\[y=x^2+C\]\[y(0)=C=0\]\[y(1)=1+C=100\to C=99\]so C is trying to be two different numbers at once, which is not possible. Not sure what you call this type of 'impossible initial values' set-up...
I think BVP's are at least second order
if it is an initial value problem then there is no solution since c cant be two different numbers at once, where as if this was a boundary problem we just identified the boundary values for the boundary conditions.
Yes, I think it is an IVP with two contradictory values. A first-order BVP doesn't really make any sense since you only need one condition to find C, and boundary conditions come in pairs or more.