[spec] start differential equations & verifying solutions

diff --git a/spec/calculus.md b/spec/calculus.md
index 9d9ed36d9d26ef611b9fc4f9d8598ab528949ff8..c6818d4a70fc710c8ac1f5a7ef5e08173d0b718e 100644 (file)
--- 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 $f$
 $$\int^b_a f(x) \> dx = F(b) - F(a)$$
 
 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.