It is easy to check that for any value of $\displaystyle {c}$, the function
$\displaystyle {y}={c}{e}^{{-{2}{x}}}+{e}^{{-{x}}}$

is a solution of the equation

$\displaystyle {y}^{{′}}+{2}{y}={e}^{{-{x}}}$.

Find the value of $\displaystyle {c}$ for which the solution satisfies the initial condition $\displaystyle {y}{\left({3}\right)}={2}$.

$\displaystyle {c}=$ Preview Question 1