Explain how to find the particular solution to each given IVP.
\[ -81 \, {x} = {x''} \hspace{2em} {x} (0)= 4 , {x} '(0)= 45 \]
\[ 0 = -{y''} - 5 \, {y} - 6 \, {y'} \hspace{2em} {y} (0)= 2 , {y} '(0)= -22 \]
Answer:
\[ {x} = 4 \, \cos\left(9 \, t\right) + 5 \, \sin\left(9 \, t\right) \]
\[ {y} = -3 \, e^{\left(-t\right)} + 5 \, e^{\left(-5 \, t\right)} \]