Exercise

1. Find the power series solution of the following differential equation around $x = 0$.
$$\begin{array}{ll} (a) \ y^{\prime} + y = e^{x} & (b) \ y^{\pr... ...(d) \ y^{\prime\prime} + xy^{\prime} - 4y = \sin{x} \end{array}$$
2. Find the power series solution of the following differential equation around the given point.
$$\begin{array}{ll} (a) \ y^{\prime\prime} + (x-2)y = 0, \ a =... ...\prime\prime} + (x-1)y^{\prime} + 3y = x^2, \ a = 1 \end{array}$$