### Differentiation : Radius of Convergence for Power Series

Consider the differnetial equation y'(x) + xy(x) = 0 with y(0) = 0 Look for a solution of this problem of the form y(x) = A + B + Ce^-x + De^-1/2x^2 Use the fact that y must satisfy the equation and the initial conditions to identify the constants A,B,C and D. By setting u = -x^2/2 in the power series for f(u) = exp{u},