<?xml version='1.0' encoding='UTF-8'?>
<exercise xmlns="https://spatext.clontz.org" version="0.0">
<statement>
<p>
Show that
<m>y_1={{y1}}</m>,
<m>y_2={{y2}}</m>, and
<m>y_3={{y3}}</m>,
are particular solutions to the following ODE:
</p>
<me>{{ode}}</me>
<p>
Then show that these solutions are independent by using the Wronskian,
and give the general solution for the ODE.
</p>
</statement>
<answer>
<me>
W({{y1}},{{y2}},{{y3}})=
{{wronskian}}
</me>
<me>
y = k_1{{y1}}+k_2{{y2}}+k_3{{y3}}
</me>
</answer>
</exercise>