We have an undamped unforced oscillator y"(t)+4 y(t) = 7 cos(2.3 t)

y(0)=0

y'(0)=0

Is this the solution to the above differential equation?

5.42636 Cos[2 t]-5.83333 Cos[0.3 t] Cos[2 t]+0.406977 Cos[2 t] Cos[4.3 t]+5.83333 Sin[0.3 t] Sin[2. t]+0.406977 Sin[2 t] Sin[4.3 t]

How can we show that it solves the DE?

What about the solution: 10.8527 Sin[0.15 t] Sin[2.15 t] ?

Where does the amplitude come from?