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A user with 908 edits. Account created on 27 February 2024.
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  • 22:4722:47, 17 April 2024 diff hist +648 N Logistic equationCreated page with "Of the form <math>\begin{cases} y' = y(1 - y)\\ y(0)=y_0 \end{cases}</math> The solution is <math>y(t) = \frac{y_0e^t}{y_0 e^t - (y_0 - 1)}</math> = Analysis = ''y'' is undefined at <math>t = \ln \left( \frac{y_0 - 1}{y_0} \right)</math> If ''0 < y_0 < 1,'' The solution is defined for all ''t.'' ''y(t)'' approaches 1 as t approaches infinity. ''y(t)'' approaches 0 as ''t'' approaches negative infinity. For ''y_0 > 1,'' the blowup time is negative <math>\ln \left(..." Tag: Visual edit
  • 21:5221:52, 17 April 2024 diff hist +111 Integrating factorNo edit summary Tag: Visual edit
  • 21:4721:47, 17 April 2024 diff hist +571 N Integrating factorCreated page with "'''Integrating factors''' is a method to solve scalar Linear First Order ODE<nowiki/>s. Consider <math>y' + p(t) y = g(t)</math> We multiply bothsides by integrating factor <math>\mu(t)</math> such that the left hand side to be the ''exact derivative of a product.'' For this to work, we need <math>\mu' = \mu p</math> Applying the integrating factor, we have <math>\begin{aligned} \mu(t) y + \mu(t) p(t) y &= \mu(t) g(t) \\ \mu y' + \mu ' y &= \mu g \\ (\mu y)' &=..." Tag: Visual edit
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