> [!NOTE] Definition (Second Order Linear Scalar Ordinary Differential Equation with Real Coefficients) > A second order linear scalar ordinary differential equation with real coefficients is a [[Second Order Linear Scalar Ordinary Differential Equation|linear second order equation]] the form $a \frac{d^{2}}{dt^{2}}x(t) +b \frac{d}{dt} x(t) + cx(t) = s(t) \tag{1}$where $0\neq a,b,c\in \mathbb{R}.$ # Properties See [[Solution to Inhomogeneous Second Order Linear Scalar Ordinary Differential Equation with Real Coefficients]]. Note that [[Reduction of Order of Scalar Ordinary Differential Equations|reduction of order]] asserts that a homogenous second order equation can be written as a $2\times 2$ [[Solution to Homogenous Linear 2 x 2 System of First Order Ordinary Differential Equations with Real Coefficients|system]] of equations with constant coefficients. # Applications **Series circuits**: [[RLC Circuit Model]]. **Oscillations**: ...