The equations presented are the same meaning that they have the same solution. Let me explain. The first one was:

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

we get:

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:

or:

Can you take it from here to show that this is the same solution as the first one?