Consider the differential equation
(x
2 + 1)y
′′ − 4xy′ + 6y = 0.
(a) Determine all singular points and find a minimum value for the
radius of convergence of
a power series solution about x0 = 0.
(b) Use a power series expansion y(x) = ∑∞
n=0
anx
n
about the ordinary point x0 = 0, to find
a general solution to the above differential equation, showing all
necessary steps including the
following:
(i) recurrence relation;
(ii) determination...
1)Find the general solution of the given second-order
differential equation.
y'' − 7y' + 6y = 0
2)Solve the given differential equation by undetermined
coefficients.
y'' + 4y = 6 sin(2x)
Find the general solution to the differential equation below.
y′′ − 6y′ + 9y = 24t−5e3
Calculate the inverse Laplace transform of ((3s-2)
e^(-5s))/(s^2+4s+53)
Calculate the Laplace transform of y = cosh(at) using the
integral definition of the Laplace transform. Be sure to note any
restrictionson the domain of s. Recall that cosh(t)
=(e^t+e^(-t))/2