2. a) Follow this procedure again to derive a power-series representation of the general solution of the differential equation y"(x) - 2xy'(x) +y(x) = 0 (Express the terms in your power series solution in such a way that the pattern is clear.) b) Derive a power-series description of the solution to the initial value problem y"(x) - 2ry'(x) + y(x) = 0, y(0) = -1, y'(0) = 1 c) Generate an approximate solution by truncating the power series representation from part (b) after the r term. Plot this truncated series over the interval r E [-3, 1] with appropriate labels on your graph. (Note: The differential equation in this case is a particular case of the Hermite equation and has applications in quantum mechanics but the solutions cannot be expressed in terms of elementary functions.)