Explain how to find the particular solution to each given IVP.
\[ {x''} + {x'} = 6 \, {x} \hspace{2em} {x} (0)= 9 , {x} '(0)= -2 \]
\[ 36 \, {y} = -{y''} \hspace{2em} {y} (0)= 0 , {y} '(0)= 18 \]
Answer:
\[ {x} = 5 \, e^{\left(2 \, t\right)} + 4 \, e^{\left(-3 \, t\right)} \]
\[ {y} = 3 \, \sin\left(6 \, t\right) \]