Homogenous ODE, How do I demonstrate a proof using a function from the ODE itself

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I have attempted this problem multiple times. I found the Wronskian and it's derivative. I am solely confused by how to use $~p(t)~$ in the proof itself. I attempted to say that $~Ay_1 + By_2~$ is also a solution. I then plugged in both the first and second derivative into the ODE and solved for $~P(t)~$ and then multiplied that by the Wronskian.

Is my approach and understanding of this problem wrong, if so, what am I misinterpreting?