Question

Use the method of variation of parameters to determine the general solution of the given differential equation.

y′′′−y′=3t

Use C1, C2, C3, ... for the constants of integration.

Answer #1

use the method of variation of parameters to determine the
general solution of the given differential equation.
y(4)+2y''+y=sin t
answer:
c1cos(t)+c2sin(t)+c3t*cos(t)+c4t*sin(t)-1/8t2sin(t)
I can't get past finding the Wronskian, not to mention w1,w2,w3,
and w4. The matrix seems way to complicated when I cross multiply
using the determinant method. Is there an easier way?

Solve the following differential equation by variation of
parameters. Fully evaluate all integrals.
y′′+9y=sec(3x).
a. Find the most general solution to the associated homogeneous
differential equation. Use c1 and c2 in your
answer to denote arbitrary constants, and enter them as c1 and
c2.
b. Find a particular solution to the nonhomogeneous differential
equation y′′+9y=sec(3x).
c. Find the most general solution to the original nonhomogeneous
differential equation. Use c1 and c2 in your
answer to denote arbitrary constants.

Use the method of variation parameters to find the
general solution of the differential equation
y'' +16y = csc 4x

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)= ?

Use variation of parameters to find a general solution to the
differential equation given that the functions y1 and y2 are
linearly independent solutions to the corresponding homogeneous
equation for t>0.
y1=et y2=t+1
ty''-(t+1)y'+y=2t2

3. Find the general solution if the given differential equation
by using the variation of parameters method. y''' + y'= 2 tan x, −
π /2 < x < π/2

Find the general solution to the following differential equation
using the method of variation of parameters.
y"-2y'+2y=ex csc(x)

a) Find the general solution of the differential equation
y''-2y'+y=0
b) Use the method of variation of parameters to find the general
solution of the differential equation y''-2y'+y=2e^t/t^3

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

This is a differential equations problem:
use variation of parameters to find the general solution to the
differential equation given that y_1 and y_2 are linearly
independent solutions to the corresponding homogeneous equation for
t>0. ty"-(t+1)y'+y=18t^3 ,y_1=e^t ,y_2=(t+1)
it said the answer to this was C_1e^t + C_2(t+1) -
18t^2(3/2+1/2t)
I don't understand how to get this answer at all

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