Difference between revisions of "Linear Homogeneous Equations"
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| − | + | Linear differential equations take the form | |
<math> P_{n}(x)y^{(n)} + P_{n-1}(x)y^{(n-1)} + ... + P_{1}(x)y' + P_{0}(x)y = Q(x) </math> | <math> P_{n}(x)y^{(n)} + P_{n-1}(x)y^{(n-1)} + ... + P_{1}(x)y' + P_{0}(x)y = Q(x) </math> | ||
where <math> P_{n}(k) </math> and <math> Q(x) </math> are functions of the independent variable x and <math> y^{k} </math> is the k-th derivative of <math> y(x) </math> with respect to x. | where <math> P_{n}(k) </math> and <math> Q(x) </math> are functions of the independent variable x and <math> y^{k} </math> is the k-th derivative of <math> y(x) </math> with respect to x. | ||
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| + | Homogeneous linear equations are linear differential equations where <math> Q(x) = 0 </math>. | ||
Latest revision as of 10:49, 20 September 2021
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 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 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
