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 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 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) 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.
(b) Find the indicial equation and its roots.
c) Determine the recurrence relation(you do NOT need to find the
solutions).
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
Consider the differential equation:
y'(x)+3xy+y^2=0.
y(1)=0. h=0.1
Solve the differential equation to determine y(1.3)
using:
a. Euler Method
b. Second order Taylor series method
c. Second order Runge Kutta method
d. Fourth order Runge-Kutta method
e. Heun’s predictor corrector method
f. Midpoint method
Consider the differential equation x′=[2 4
-2 −2],
with x(0)=[1 1]
Solve the differential equation where x=[x(t)y(t)].
x(t)=
y(t)=
please be as clear as possible especially when solving for c1
and c2 that's the part i need help the most