From 0706032a9fcf3d161518f38cd42849810f6619ed Mon Sep 17 00:00:00 2001 From: Sasserisop Date: Thu, 19 Oct 2023 19:53:20 -0600 Subject: [PATCH] fixed bernoulli and renamed heaviside link --- ...(lec 18).md => (Heaviside) Unit step function (lec 18).md} | 0 content/Bernoulli equations (lec 3).md | 4 ++-- 2 files changed, 2 insertions(+), 2 deletions(-) rename content/{Heaviside Unit step function (lec 18).md => (Heaviside) Unit step function (lec 18).md} (100%) diff --git a/content/Heaviside Unit step function (lec 18).md b/content/(Heaviside) Unit step function (lec 18).md similarity index 100% rename from content/Heaviside Unit step function (lec 18).md rename to content/(Heaviside) Unit step function (lec 18).md diff --git a/content/Bernoulli equations (lec 3).md b/content/Bernoulli equations (lec 3).md index 6a8f039..a205106 100644 --- a/content/Bernoulli equations (lec 3).md +++ b/content/Bernoulli equations (lec 3).md @@ -17,8 +17,8 @@ $y^{-n}\frac{ dy }{ dx }=\frac{ du }{ dx }{\frac{1}{1-n}}$ substituting in we get: $y^{-n}\frac{ dy }{ dx }+P(x)u=Q(x)=\frac{ du }{ dx }{\frac{1}{1-n}+P(x)u}$ -and we get a linear equation again: (Handy formula if you wanna solve specific Bernoulli equations quick.) -$$\frac{1}{1-n}\frac{ du }{ dx }+P(x)=Q(x)\quad \Box$$ +and we get a linear equation again: (Handy formula if you wanna solve Bernoulli equations quick. Just remember that once you find $u(x)$, substitute it back for $y(x)^{1-n}=u(x)$ to get your solution for y.) +$$\frac{1}{1-n}\frac{ du }{ dx }+P(x)u=Q(x)\quad \Box$$ >Remember when I said that when n=1 the equation becomes a separable equation?: >$y^{-n}\frac{ dy }{ dx }+P(x)y^{1-n}=Q(x)$ >let $n=1$