find the general solution of the given differential equation
1. 2y''+3y'+y=t^2 +3sint
find the solution of the given initial value problem
1. y''−2y'−3y=3te^2t, y(0) =1, y'(0) =0
2. y''−2y'+y=te^t +4, y(0) =1, y'(0) =1
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
1) . Solve the IVP:
y^''+6y^'+5y=0, y(0)=1, y^' (0)=3
2. Find the general solution to each of the following:
a) y^''+2y^'+5y=e^2x
b) y^''+2x/(x^2+1) y'=x
c) y^''+4y=1/(sin(2x)) (use variation of parameters)
Given the differential equation y’’ +5y’+6y=te^t with start
value y(0) = 0 and y’(0). Let Y(s) be the Laplace transformed of
y(t).
a) Find an expression for Y(s)
b) Find the solution to the equation by using inverse Laplace
transform.