1. Find the general solution to the following ODE:
y′′′+ 4y′= sec(2x)
2. Find the solution to the following IVP:
2y′′+ 2y′−2y= 6x2−4x−1
y(0) = −32
y′(0) = 5
3. Verify that y1=x1/2ln(x) is a solution
to
4x2y′′+y= 0,
and use reduction of order to find a second solution
y2.
4.
Find the general solutions to the following ODEs:
a) y′′′−y′= 0.
b) y′′+ 2y′+y= 0.
c) y′′−4y′+ 13y= 0.
Find the general solution y(t) to the following ODE using (a)
Method of Undetermined Coefficients AND (b) Variation of
Parameters:
2y"-y'+5y = cos(t) - et Sin(t)
a) verify that y1 and y2 are fundamental solutions
b) find the general solution for the given differential
equation
c) find a particular solution that satisfies the specified
initial conditions for the given differential equation
1. y'' + y' = 0; y1 = 1 y2 = e^-x; y(0) = -2 y'(0) = 8
2. x^2y'' - xy' + y = 0; y1 = x y2 = xlnx; y(1) = 7 y'(1) =
2