Study of equations involving derivatives and their applications.
These equations involve the second derivative, like \( y'' \) or \( \frac{d^2y}{dx^2} \).
\( a\frac{d^2y}{dx^2} + b\frac{dy}{dx} + cy = f(x) \)
Here, \( a \), \( b \), and \( c \) are constants.
These equations describe systems with acceleration, like springs or circuits.
\[a\frac{d^2y}{dx^2} + b\frac{dy}{dx} + cy = f(x)\]
A mass on a spring: \( m\frac{d^2x}{dt^2} + kx = 0 \)
An electrical circuit with a resistor, capacitor, and inductor.
Second-order equations handle problems involving acceleration or curvature.