From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Wed, 15 May 2019 04:06:32 +0000 (+1000)
Subject: [spec] start differential equations & verifying solutions
X-Git-Tag: yr12~135
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/55440b433433679457193c6eef12e9a2df17c5c5

[spec] start differential equations & verifying solutions
---

diff --git a/spec/calculus.md b/spec/calculus.md
index 9d9ed36..c6818d4 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -384,3 +384,15 @@ If $f$ is continuous on $[a, b]$, then
 $$\int^b_a f(x) \> dx = F(b) - F(a)$$
 
 where $F$ is any antiderivative of $f$
+
+## Differential equations
+
+One or more derivatives
+
+**Order** - highest power inside derivative  
+**Degree** - highest power of highest derivative  
+e.g. ${\left(dy^2 \over d^2 x\right)}^3$: order 2, degree 3
+
+### Verifying solutions
+
+Start with $y=\dots$, and differentiate. Substitute into original equation.