24.T Second-order homogeneous linear differential equations
Reference: Stewart 15.5, 6.7
Keywords: Second-order equations, characteristic equation,
homogeneous equations, hyperbolic sine and cosine functions
Learning Objectives: The student will be able to:
- Recognize second-order linear differential equations
- Solve equations of the form ay" + by' + cy = 0,
where a, b, c are constants, by looking for solutions of the form
y=erx, where r is a constant
- Handle the three cases of solutions to the characteristic equation
ar2 + br + c = 0:
real and unequal roots, real and equal roots, and complex roots
- Use linear combinations of solutions to obtain the general solution
- Solve initial value problems involving these differential equations
- Express solutions using hyperbolic sine and cosine, when appropriate
24.R Second-order nonhomogeneous linear equations;
Applications of second-order ODEs
Reference: Stewart 15.6, 15.7
Keywords: Nonhomogeneous, method of undetermined coefficients,
harmonic motion, damped and undamped vibrations, spring-mass system,
RLC series circuit
Learning Objectives: The student will be able to:
- Solve nonhomogeneous linear differential equations by the method of
undetermined coefficients
- Solve initial value problems for second-order nonhomogeneous equations
- Set up and solve initial value problems for vibrating
spring-mass systems, with and without damping,
and with and without an applied force.
- Set up and solve initial value problems for series RLC electrical circuits