Difference between revisions of "Linear Homogeneous Equations"

Latest revision as of 10:49, 20 September 2021

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 $Q(x)=0$ .

@@ Line 1: / Line 1: @@
-Homogeneous linear differential equations take the form
+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.
+Homogeneous linear equations are linear differential equations where <math> Q(x) = 0 </math>.
 ==Resources==
 * [https://web.stanford.edu/class/archive/math/math21/math21.1146/files/21/notes8.pdf Homogeneous Linear Differential Equations], Stanford University
+* [https://www.whitman.edu/mathematics/calculus_online/section17.02.html First Order Homogeneous Linear Equations], Whitman College