Explain how to find the particular solution to each given IVP.
\[ -{x''} = 4 \, {x} \hspace{2em} {x} (0)= -4 , {x} '(0)= 0 \]
\[ 2 \, {y} = -{y''} + 3 \, {y'} \hspace{2em} {y} (0)= -8 , {y} '(0)= -13 \]
Answer:
\[ {x} = -4 \, \cos\left(2 \, t\right) \]
\[ {y} = -5 \, e^{\left(2 \, t\right)} - 3 \, e^{t} \]