Assume that $y$ is the solution of the initial-value problem $$y' - 3 y = \begin{cases} \frac{4\sin x}{x} & x \ne 0 \\ 4 & x = 0 \end{cases}\;, \qquad y(0) = 1 \;.$$ If $y$ is written as a power series $$y = \sum_{n=0}^\infty c_nx^n\;,$$ then
$y =$ + $x$ + $x^2$ + $x^3$ + $x^4 + \cdots$ .

Note: You do not have to find a general expression for $c_n$. Just find the coefficients one by one.