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[SOLVED] 2nd order to 1st order 2

dwsmith

Well-known member
Feb 1, 2012
1,673
\begin{alignat*}{3}
m\ddot{x} & = & -c(y)\sqrt{x^2+y^2}x\\
m\ddot{y} & = & -mg - c(y)\sqrt{x^2 + y^2}y
\end{alignat*}
where $c(y) = 0.25\text{N}\cdot\text{s}^2/\text{m}^4\cdot (15\text{cm})^2\exp(-y/(10000\text{m}))$
In order to re-write this as a system of 1st order ODEs, do I have to put everything in the right dimensions like all meters or centimeter measurements first?