It is easy to check that for any value of 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 $\displaystyle {y}{\left(-{1}\right)}={1}$.

$\displaystyle {c}=$ Preview Question 6