From: Andrew Lorimer 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 [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 $A$.