Given that x =0 is a regular singular point of the given
differential equation, show that the indicial roots of the
singularity differ by an integer. Use the method of Frobenius to
obtain at least one series solution about x = 0.
xy"+(1-x)y'-y=0
Determine a differential equation that has x = 0 as a regular
singular point and that the roots of the index equation are i and
i. Find a solution around x = 0.
Consider the equation xy′′+y′+y= 0, x >0.
a) Verify that 0 is a regular singular point.
(b) Find the indicial equation and its roots.
c) Determine the recurrence relation(you do NOT need to find the
solutions).
Determine if x = 0 is an ordinary point, regular singular point, or
irregualr singlar point for the following. Make sure to give
reasons.
a) y" + (2/x)y' + (5e^x)y = 0
b) x(1-x)y" + 4y' + y =0
its
3xy, no y by itself
(a) Find the equation of the plane passing through the point
P(0, 0, 5) and the line x = 1 + t, y = 1 − t, z = 4 − 5t.
(b) Find parametric equations for the line passing through point
(1, 2, 3) and parallel to the line x = 2 − 3t, y = 4 + t, z =
2t.