Question

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

y^{(4)}+2y''+y=sin t

answer:
c_{1}cos(t)+c_{2}sin(t)+c_{3}t*cos(t)+c_{4}t*sin(t)-1/8t^{2}sin(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?

Answer #1

Now if you have any doubt then leave a comment I'll try to resolve it.

Please give me thumb's up I really need it.

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.

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 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 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

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)= ?

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

Solve the following second order differential equations:
(a) Find the general solution of y'' − 2y' = sin(3x) using the
method of undetermined coefficients.
(b) Find the general solution of y'' − 2y'− 3y = te^−t using the
method of variation of parameters.

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

differential equations!
find the Differential Equation General Solve by using
variation of parameters method...
y''' - 3y'' +3y' - y =12e^x

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