Find the infinite series for the following differential equation
about x = 0, using Frobenius method, Bessel's or Legrende's
equations.
x^2y" + 4xy' + (2+x)y = 0
Use an appropriate infinite series method about
x = 0
to find two solutions of the given differential equation. (Enter
the first four nonzero terms for each linearly independent
solution, if there are fewer than four nonzero terms then enter all
terms. Some beginning terms have been provided for you.)
y'' − xy' − 3y = 0
y1
=
1
+
3
2
x2 + + ⋯
y2
=
x
+
+ ⋯
Use the method of Frobenius to obtain two linearly independent
series solutions about x = 0. Form the general solution on
(0,inf).
2x^2y'' - xy' + (x^2 + 1)y = 0
Find the infinite series solution about x = 0 for the following
DE, using Bessel's, Legrende's, or Frobenius method equations.
3x^2y" + 2xy' + x^2y = 0
Find the first 4 non-zero terms in the series expansion. Do not
use k=n substitutions
Predict the form of the solution (study limits) and find all of
the solutions using the Frobenius method approach. Write indicial
equation, find its roots, the recurrence relation, and the first
four terms terms of each series solution for xy"+y'+x^2y=0
a. Seek power series solutions of the given differential
equation about the given point x0; find the recurrence relation
that the coefficients must satisfy.
b. Find the first four nonzero terms in each of two solutions y1
and y2 (unless the series terminates sooner).
y''-xy'-y=0 ; x0=0