Explain how to find the particular solution to each given IVP.
\[ 6 \, {x'} - 8 \, {x} = {x''} \hspace{2em} {x} (0)= 3 , {x} '(0)= 10 \]
\[ -64 \, {y} = {y''} \hspace{2em} {y} (0)= 2 , {y} '(0)= -32 \]
Answer:
\[ {x} = 2 \, e^{\left(4 \, t\right)} + e^{\left(2 \, t\right)} \]
\[ {y} = 2 \, \cos\left(8 \, t\right) - 4 \, \sin\left(8 \, t\right) \]