ODEs 1

• 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?