# Convert the differential equation u''-u'-2u=e^{-5t} into a system of first

Convert the differential equation $u{}^{″}-{u}^{\prime }-2u={e}^{-5t}$ into a system of first order equations by letting x=u, y=u'
${x}^{\prime }=?$
${y}^{\prime }=?$

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Archie Jones
Given $u{}^{″}-{u}^{\prime }-2u={e}^{-5t}$
Suppose x=u, y=u',
x'=u' and y'=u''
and
and
Therefore, the system of first order differential equations is,
x'=y
${y}^{\prime }=y+2x+{e}^{-5t}$