Explain how to find the particular solution to each given IVP.

  1. \[ 0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em} {x} (0)= 4 , {x} '(0)= 10 \]

  2. \[ -100 \, {y} = {y''} \hspace{2em} {y} (0)= 3 , {y} '(0)= -30 \]

Answer:

\[ {x} = 3 \, e^{\left(3 \, t\right)} + e^{t} \]

\[ {y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, t\right) \]