fythynwyrk0

2022-07-04

Express the differential equation
${y}^{‴}-6{y}^{″}-{y}^{\prime }+6y=0$
as a system of first order equations i.e. a matrix equation of the form
$A\left(\stackrel{\to }{x}{\right)}^{\prime }=0$
where

Elliott Gilmore

Expert

Here how you advance, let y'=z, then we will have the system
${z}^{″}-6{z}^{\prime }-z+6y=0\phantom{\rule{0ex}{0ex}}{y}^{\prime }=z$
Again, put z'=w which results in the system
${w}^{\prime }-6w-z+6y=0\phantom{\rule{0ex}{0ex}}{z}^{\prime }=w\phantom{\rule{0ex}{0ex}}{y}^{\prime }=z$
Arranging the above equation gives
${y}^{\prime }=z\phantom{\rule{0ex}{0ex}}{z}^{\prime }=w\phantom{\rule{0ex}{0ex}}{w}^{\prime }=6w+z-6y.$
Now, I am sure you know how to write this in a matrix form.

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