Linear Differential Equations

Vocabulary flashcards defining fundamental concepts of first-order and second-order linear differential equations.

Cauchy problem (first-order)

A first-order linear differential equation $(E): y' + a(x)y = b(x)$ paired with an initial condition $y(x_0) = y_0$ for $x_0 \in I$, which admits a unique solution given continuous functions $a$ and $b$.

Characteristic equation

The polynomial equation $x^2 + ax + b = 0$ associated with the second-order linear homogeneous differential equation with constant coefficients $(E_0): y'' + ay' + by = 0$.