Linear Homogeneous Equations

Linear differential equations take the form

$P_{n}(x)y^{(n)}+P_{n-1}(x)y^{(n-1)}+...+P_{1}(x)y'+P_{0}(x)y=Q(x)$

where $P_{n}(k)$ and $Q(x)$ are functions of the independent variable x and $y^{k}$ is the k-th derivative of $y(x)$ with respect to x.

Homogeneous linear equations are linear differential equations where $Q(x)=0$.

Resources

• Homogeneous Linear Differential Equations, Stanford University
• First Order Homogeneous Linear Equations, Whitman College