11.1 Characterizing ODEs (3 pts)
For each of the following three ODEs ...
i. Characterize its order (e.g. 1st-order, 2nd-order, etc.)
ii. Characterize it as an IVP (Initial Value Problem) or BVP (Boundary Value Problem),
iii. Write it in standard form.
(A) $y^2 \frac{dy}{dt} + 1 = y + t \frac{d^3y}{dt^3}$, $y(1) = 1$, $y'(1) = 0$, $y''(1) = 3$
(B) $\frac{1}{Q} \frac{d(Q^3)}{dt} + Q \frac{dQ}{dt} - t = 0$, $Q(0) = 1$
(C) $(ln x)\frac{d^2w}{dx^2} + w + 5\frac{dw}{dx} = sin(w)$, $w(0) = 1$, $w'(5) = 0$
