a$)$ Consider the second order ODE

$\frac{d^{2}y}{d{x}^2}+10\frac{dy}{dx}+21y=0$

Find the general solution by trying solutions of the form $y=e^x$ and using the characteristic equation.

b$)$ Use your result from part a$),$ find the general solution to

$\frac{d^{2}y}{d{x}^2}+10\frac{dy}{dx}+21y=3e^{-x}$

Find the particular solution for which $y(0)=y^{\text{'}}(0)=0.$