From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Thu, 16 May 2019 06:27:51 +0000 (+1000)
Subject: [spec] DEs of the dependent variable
X-Git-Tag: yr12~133
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/a978febdd78ca197ca9572dfcb86e1cf7249fdc6?ds=inline

[spec] DEs of the dependent variable
---

diff --git a/spec/calculus.md b/spec/calculus.md
index c6818d4..30a2957 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -396,3 +396,7 @@ 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.
+
+### Function of the dependent variable
+
+If ${dy \over dx}=g(y)$, then ${dx \over dy} = 1 \div {dy \over dx} = {1 \over g(y)}$. Integrate both sides to solve equation. Only add $c$ on one side. Express $e^c$ as $A$.