7. Homogeneous Second Order Linear Differential Equations with Constant Coefficients

Constant Coefficients

Definition

The equation $a{y}^{\prime \prime }(x)+b{y}^{\prime }(x)+cy(x)=0$ is called a homogeneous, linear, second-order differential equation with constant coefficients.

Example

Mass-spring-damper model

$m{u}^{\prime \prime }(t)+c{u}^{\prime }(t)+ku(t)=0$

Ansatz is the educated guess of the shape.