Explain how to find the particular solution to each given IVP.
\[ {x''} - 2 \, {x'} = 3 \, {x} \hspace{2em} {x} (0)= -1 , {x} '(0)= -19 \]
\[ 0 = -25 \, {y} - {y''} \hspace{2em} {y} (0)= -4 , {y} '(0)= 5 \]
Answer:
\[ {x} = -5 \, e^{\left(3 \, t\right)} + 4 \, e^{\left(-t\right)} \]
\[ {y} = -4 \, \cos\left(5 \, t\right) + \sin\left(5 \, t\right) \]