Explain how to find the particular solution to each given IVP.
\[ 0 = {x''} + 4 \, {x} \hspace{2em} {x} (0)= 3 , {x} '(0)= -8 \]
\[ 7 \, {y'} = {y''} + 10 \, {y} \hspace{2em} {y} (0)= -3 , {y} '(0)= -3 \]
Answer:
\[ {x} = 3 \, \cos\left(2 \, t\right) - 4 \, \sin\left(2 \, t\right) \]
\[ {y} = e^{\left(5 \, t\right)} - 4 \, e^{\left(2 \, t\right)} \]