Question

Use variation of parameters to find a particular solution
x_{p}.

x'' + 2x' + x = 6e^{−t}, x_{1}(t) =
e^{−t}, x_{2}(t) = te^{−t}

x_{p}(t) = ________________

Answer #1

use variation of parameters to find a particular solution
y'' + y' +12y = xe2x
y1 =
e3x
y2 =
e-2x

y′′ + 4y′ + 5y = e−2x sin x
(c) Find the particular solution yp(t) using the Variation of
Parameters method

Use the method of variation of parameters to find a particular
solution of the differential equation y′′−8y′+15y=32et.

use variation of parameters to determine a particular solution
to the given equation y'''-3y''+3y'-y=e^x

Find the method by the Variation of Parameters
y'' - 4y' +4y = (e^(2x))/x

Find only the particular solution of the given differential
equation by using variation of parameters and Wronskians.
y ' ' - y = csc x cot x

Find a particular solution for the differential equation by
variation of parameters.
y''- y' -2y = e^3x , y(0) = -3/4 , y'(0)=15/4

Use either the method of undetermined coefficients or
method of variation of parameters to find the general solution.
dx/dt = 3x - 2y + e^t
dy/dt = x

Use variation of parameters to find a general solution to the
differential equation given that the functions y 1 and y 2 are
linearly independent solutions to the corresponding homogeneous
equation for t>0.
ty"-(t+1)y'+y=30t^2 ; y1=e^t , y2=t+1
The general solution is y(t)= ?

Using variation of parameters, find a particular solution of the
given differential equations:
a.) 2y" + 3y' - 2y = 25e-2t (answer should be: y(t) =
2e-2t (2e5/2 t - 5t - 2)
b.) y" - 2y' + 2y = 6 (answer should be: y = 3 + (-3cos(t) +
3sin(t))et )

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