Question
In: Advanced Math
Determine if x = 0 is an ordinary point, regular singular point, or irregualr singlar point...
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
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Determine a differential equation that has x = 0 as a regular singular point and that...
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.
given DE has a regular singular point at x=0 determine two solutions for x>0 x^2y''+3xy'+(1+x)y=0
given DE has a regular singular point at x=0 determine
two solutions for x>0
x^2y''+3xy'+(1+x)y=0
Given that x =0 is a regular singular point of the given differential equation, show that...
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
(a) Show that x= 0 is a regular singular point. (b) Find the indicial equation and...
(a) Show that x= 0 is a regular singular point.
(b) Find the indicial equation and the indicial roots of it.
(c) Use the Frobenius method to and two series solutions of each
equation
x^2y''+xy'+(x^2-(4/9))y=0
Consider the equation xy′′+y′+y= 0, x >0. a) Verify that 0 is a regular singular point....
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).
Find two linearly independent solutions near the regular singular point x₀= 0 x²y'' + (6x +...
Find two linearly independent solutions near the regular
singular point x₀= 0
x²y'' + (6x + x²)y' + xy = 0
Consider the second-order differential equation x2y′′+(x2+ax)y′−axy=0 where a=−2 Is x0=0 a singular or ordinary point of...
Consider the second-order differential equation
x2y′′+(x2+ax)y′−axy=0 where a=−2 Is x0=0 a singular or ordinary
point of the equation? If it is singular, is it regular or
irregular? Find two linearly independent power series solutions of
the differential equation. For each solution, you can restrict it
to the first four terms of the expansion
Q: Find the power series solution centered at the ordinary point x = 0 for each...
Q: Find the power series solution centered at the ordinary point
x = 0 for each equation.
((x^2) + 1) y''-6y=0
Determine if the language ?={?^?∶?=?^3????????≥0}over Σ={?}is regular.
Determine if the language ?={?^?∶?=?^3????????≥0}over Σ={?}is
regular.
Find expansion of A) tan (x) about point x=0 B) cos (x) about point x=0 C)...
Find expansion of
A) tan (x) about point x=0
B) cos (x) about point x=0
C) (1+x)^1/2 about point x=0
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