A. Find a particular solution to the nonhomogeneous differential
equation y′′ + 4y′ + 5y = −15x
+ e-x
y =
B. Find a particular solution to
y′′ + 4y = 16sin(2t).
yp =
C. Find y as a function of x if
y′′′ − 10y′′ + 16y′ =
21ex,
y(0) = 15, y′(0) = 28,
y′′(0) = 17.
y(x) =
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
(a) Write a general expression for yp(x) a particular
solution to the nonhomogeneous
differential equation [Do not evaluate the coefficients]
y′′ + 2y′ + 2y = e-x (4x + sin x) + 2 cos(2x).
(b) Solve the initial value problem
y′′ - y = 1 + 4ex; y(0) = 1; y′(0) = 2:
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 a general solution to the differential equation using the
method of variation of parameters.
y''+ 25y= sec5t
The general solution is y(t)= ___
y''+9y= csc^2(3t)
The general solution is y(t)= ___