Explain how to find the particular solution to each given IVP.
\[ 25 \, {x} + {x''} = 0 \hspace{2em} {x} (0)= -5 , {x} '(0)= -15 \]
\[ -3 \, {y} - 2 \, {y'} = -{y''} \hspace{2em} {y} (0)= -5 , {y} '(0)= -3 \]
Answer:
\[ {x} = -5 \, \cos\left(5 \, t\right) - 3 \, \sin\left(5 \, t\right) \]
\[ {y} = -2 \, e^{\left(3 \, t\right)} - 3 \, e^{\left(-t\right)} \]