Use chain rule to verify that every function of the form
y = a sin (5t) + b cos (5t)
is a solution to the differential equation
d^2y/dt^2 = -25y.
Then use this fact to find the solution which also satisfies the initial conditions:
y(0) = 3 and y'(0) = 0
(^ means exponent and d^2y is over dt^2)
The chain rule is applied to finding a derivative. The solution is detailed and well presented.