5) Second Order ODEs

Question 1

What is an Initial-Value Problem (IVP) and a
Boundary-Value Problem (BVP)

Answer 1

• Initial-Value Problem - all constraints are applied at the same value
• e.g U(0) = 0, U˙(0)
• Boundary-Value Problem - constraints are applied at different values
• e.g y(0) = 1, y(1) = 2

Question 2

How do you solve a homogenous linear, second-order ODE

Answer 2

Solve the characteristic polynomial

Question 3

What are the different forms of the answer to solving a homogenous linear, second-order ODE

Answer 3

Question 4

What is the general procedure to solve an inhomogenous linear second order ODE

Answer 4

1. Solve the characteristic polynomial
2. Choose a suitable form for the particular solution
3. Substitute yP(x) into equation to find the unknown constants {Cm}
4. General solution y(x) = yH(x) + yP(X)

Question 5

How do you solve a linear, 2nd-order ODE with a trigonemtric constant

Answer 5

Write the constant in terms of complex variables
e.g