The ODE is ln (x) y?? + 1/2 y? + y = 0.
Procedure: Show that this equation has a regular singular point at x = 1. Determine the
roots of the indicial equation there. Determine the first three non–zero terms in the series
summation n=0 to ? [a(sub)n * (x - 1)^r+n ]
corresponding to the larger root. Take x - 1 > 0. What would you
expect the radius of convergence of the series to be? Why?
So far we found that it has a regular singular point at x=1 because P(1)=0 and limx->1 for (x-1)*P(x)/Q(x) exist and limx->1 for (x-1)^2 * P(x)/R(x) exist
Once we take the derivative of the Series summation n=0 to ? [a(sub)n * (x - 1)^r+n ] and try to plug it into the equation we do not know how to multiply the power series of ln(x) by y'' series summation?
Any help on multiplying the series or how to solve this problem is much appreciated.
Procedure: Show that this equation has a regular singular point at x = 1. Determine the
roots of the indicial equation there. Determine the first three non–zero terms in the series
summation n=0 to ? [a(sub)n * (x - 1)^r+n ]
corresponding to the larger root. Take x - 1 > 0. What would you
expect the radius of convergence of the series to be? Why?
So far we found that it has a regular singular point at x=1 because P(1)=0 and limx->1 for (x-1)*P(x)/Q(x) exist and limx->1 for (x-1)^2 * P(x)/R(x) exist
Once we take the derivative of the Series summation n=0 to ? [a(sub)n * (x - 1)^r+n ] and try to plug it into the equation we do not know how to multiply the power series of ln(x) by y'' series summation?
Any help on multiplying the series or how to solve this problem is much appreciated.