Difference between revisions of "Linear Homogeneous Equations"

Revision as of 10:44, 20 September 2021

Homogeneous 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.

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 Homogeneous 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.