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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_{n}(k) } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q(x) } are functions of the independent variable x and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y^{k} } is the k-th derivative of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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