From a978febdd78ca197ca9572dfcb86e1cf7249fdc6 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Thu, 16 May 2019 16:27:51 +1000 Subject: [PATCH 1/1] [spec] DEs of the dependent variable --- spec/calculus.md | 4 ++++ 1 file changed, 4 insertions(+) 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 $A$. -- 2.43.2