book:chap4:4.3_separation_of_variables
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book:chap4:4.3_separation_of_variables [2021/12/06 14:57] – [4.3.3 Relation to free fall] abril | book:chap4:4.3_separation_of_variables [2024/01/31 23:30] (current) – fix link in footnote jv | ||
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- | ===== 4.3 Separation of variables | + | ===== 4.3 Separation of variables |
The settling of a ball in a viscous medium can be described by the equations of motion | The settling of a ball in a viscous medium can be described by the equations of motion | ||
Line 125: | Line 125: | ||
The solution of the differential equation | The solution of the differential equation | ||
\begin{align*} | \begin{align*} | ||
- | \frac{\mathrm{d} y(x)}{\mathrm{d} x} = \frac{ \mathrm{e}^{ y^2(x) } }{ 1-2 \, y^2(x) } | + | \frac{\mathrm{d} y(x)}{\mathrm{d} x} = \frac{ \mathrm{e}^{ |
\qquad\text{with}\quad y(0) = 0 | \qquad\text{with}\quad y(0) = 0 | ||
\end{align*} | \end{align*} | ||
Line 413: | Line 413: | ||
and this time the bullet will have dropped by a distance | and this time the bullet will have dropped by a distance | ||
$ g\, | $ g\, | ||
- | which is deeper than the deepest point in our Oceans.((In [[book: | + | which is deeper than the deepest point in our Oceans.((In |
+ | [[book: | ||
</ | </ | ||
book/chap4/4.3_separation_of_variables.1638799023.txt.gz · Last modified: 2021/12/06 14:57 by abril