Question

Differential equation.(see attachment)

Answer 1

Well, you have a second order homogeneous equation. So convert it to the characteristic polynomial.
\[\lambda^2+\frac{1}{RC}=0\]
This implies that:
\[\lambda=\pm \frac{1}{RC}i\]
Which gives your the solution the form of:
\[y(t)=A \sin(\frac{t}{RC})+B \cos(\frac{t}{RC})\]
Then for the second part, just plug in the initial value.