In: Advanced Math
Determine a lower bound for the radius of convergence of series solutions about each given point x0 for the given differential equation.
(1 + x^3)y'' + 4xy' + 6xy = 0
x0 = 0. x0 = 4
Solution:-
Given that
or,
Here
and
and
p(x) and q(x) has singular point when
For,
Distance from 0 to -1 is | (-1 - 0)| = 1
and distance in the complex domain from to
is
The lower bound for the radius of convergence of series solution
about
is 1
lower bound for
is 1.
For
The distance from 4 to -1 is |4 - (-1)| = 5
The distance in the complex domain from 4 to
is
and min
is
Lower bound for
is
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