# Second order linear differential equations

Learning objectives

• Discuss the equation $y^{\prime\prime} + p(t) y^\prime + q(t) y = 0$
• Solutions form 2D vector space
• Unique solution when $y(0)$ and $y^\prime(0)$ are specified.
•  Solve constant coefficient equations
• Develop computational facility with complex numbers and exponentials
• Explore solutions of the driven equation $y^{\prime\prime} + p(t) y^\prime + q(t) y = f(t)$
• frequency response of damped harmonic oscillator

Before Class

In class