For the following differential equation
y'' + 9y = sec3x,
(a) Find the general solution yh, for the
corresponding homogeneous ODE.
(b) Use the variation of parameters to find the
particular solution yp.
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
Consider the differential equation
y′(t)+9y(t)=−4cos(5t)u(t),
with initial condition y(0)=4,
A)Find the Laplace transform of the solution
Y(s).Y(s). Write the solution as a single
fraction in s.
Y(s)= ______________
B) Find the partial fraction decomposition of Y(s). Enter all
factors as first order terms in s, that is, all terms
should be of the form (c/(s-p)), where c is a constant and the root
p is a constant. Both c and p may be complex.
Y(s)= ____ + ______ +______
C)...