Find the General Solutions to the given differential equations
y(t) =
a) 6y' +y = 7t^2
b) ty' − y =
9t2e−9t, t > 0
c) y' − 8y = 9et
d)
y' + y/t = 6 cos
5t, t
> 0
Find a particular solution to the following non homogenous
equations
1) y''' + y = t^3 + sin (t) + 11e^t
2) y'' + y = 2tsin(t)
3) y''''' - 4 y''' = e^2t + t^2 +5t + 4
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
6) a) Find the general solution to the 2nd order
differential equation
y''+6y'+8y=0
[8 pts]
b) Find the general solution to
y''+6y'+8y=2e-x.
Use the method of undetermined coefficients. [8
pts]
c) Solve the IVP
y''+6y'+8y=2e-x,
y0=0,
y'0=0
[5 pts]