and has as solution:
This is easily found because it is a homogeneous second order DE with constant coefficients. Now if we multiply this DE with
which can be rewritten as:
or, after integrating:
with c the integration constant. This equation has the same solution as the first one, indeed, extracting the derivative gives:
and this can be integrated again to give:
Can you take it from here to show that this is the same solution as the first one?