Explain how to find the particular solution to each given IVP.
\[ 100 \, {x} = -{x''} \hspace{2em} {x} (0)= -2 , {x} '(0)= -50 \]
\[ {y''} + 3 \, {y'} = 10 \, {y} \hspace{2em} {y} (0)= 7 , {y} '(0)= -14 \]
Answer:
\[ {x} = -2 \, \cos\left(10 \, t\right) - 5 \, \sin\left(10 \, t\right) \]
\[ {y} = 3 \, e^{\left(2 \, t\right)} + 4 \, e^{\left(-5 \, t\right)} \]