- Write the general form of an ODE
- What is the order of this ODE: $y^\prime+ 2y^{\prime\prime} = xy^3.$
- What is the difference between the order of an ODE and the truncation error of a finite difference approximation?
- If we have a third order ODE, how many boundary conditions will we have?
- Which of the following are linear and which are nonlinear ODEs:
- $y^\prime + \alpha y = f(t)$, $\alpha$ is constant
- $yy^\prime + \alpha y = 0$, $\alpha$ is constant
- $y^\prime + \alpha(t) y = f(t)$, $\alpha$ is a function of $t$
- $y^\prime + \alpha(y) y = f(t)$, $\alpha$ is a function of $y$
- What are the two classes of ODEs, how do they differ?
- Write the advancement equation for Explicit Euler.
- Why is it called explicit?
- Write the advancement equation for Implicit Euler.
- Why is it called implicit?
- What are the orders of EE and IE?