Second order Differential equation:
Find the general solution to [ y'' + 6y' +8y = 3e^(-2x) + 2x ]
using annihilators method and undetermined coeficients.
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]
find the general solution of the given differential
equation.
1. y'' + y = tan t, 0 < t < π/2
2. y'' + 4y' + 4y = t-2 e-2t , t >
0
find the solution of the given initial value problem.
3. y'' + y' − 2y = 2t, y(0) = 0, y'(0) = 1