In that sense, section 2 is dedicated to power series solutions of homogeneous differential equations in the neighborhood of an ordinary point. In section 3 we study non homogeneous equations, also in the neighborhood of an ordinary point.
Power series solutions of differential equations in the neighborhood of an ordinary point.
Use a power series in the neighborhood of ordinary point x = 0 to demonstrate that general solution of the equation y" + xy' + y = 0, can be written by means of the following power series:
Build a program which allows you to find the solution of a second order differential equation by means of a power series in the neighborhood of ordinary point x = 0.
Assuming that function h(x) has a Taylor series in the neighbourhood of an ordinary point [x.sub.0] = 0 which converges for [absolute value of x] [down arrow] < [rho], with [rho] > 0, i.e.
Build a program that allows you to obtain and draw the graph of particular solutions of differential equation y" = P(x)y' + Q(x)y, using power series in the neighborhood of ordinary point x = 0 and given specific values for coefficients [a.sub.0] and [a.sub.1].