Linear Homogeneous Equations

Linear differential equations take the form

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}(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 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) = 0 } .

Resources

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