A laguerre equation is any differential equation of the form
xy"+(1-x)y'+ny=0 where n is an integer. Solve the Laguerre equation
with n = 1, that is solve xy"+(x-1)y'+y=0 about the singlular point
x=0.
Consider the following equation: (3 − x^2 )y'' − 3xy' − y = 0
Derive the general solution of the given differential equation
about x = 0. Your answer should include a general formula for the
coefficents.
Find the power series solution for the equation y'' + (sinx)y =
x; y(0) = 0; y'(0) = 1
Provide the recurrence relation for the coefficients and derive
at least 3 non-zero terms of the solution.
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).
For the following causal difference equation,
given that y[-1] = 0, y[-2] = 1, and x[n] = u[n], solve using
z-Transforms.
(Hint: convert to delay operator form, find the z-Transform, use
PFE to find the inverse z-Transform)
4y[n + 2] + 4y[n + 1] + 2y[n] = x[n + 1]