Assignment:
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}, determine a power series for y(x). What is the radius of convergence of the power series for y(x)?
Provide complete and step by step solution for the question and show calculations and use formulas.