Question

Find the general solution to the differential equation y′′+ 2y′= 3 + 4 sin 2t.(Hint: Variation of parameters requires integration by parts, so undetermined coefficientsis recommended—however, be careful.)

Answer #1

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

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.

Find a solution to y^''-4y^'-5y=2e^2t using variation of
parameters. Find the solution to the differential equation in
problem 6, this time using the method of undetermined
coefficients.

Find the general solution using Variation of
Parameters.
y''-y'-2y=2e^(2t)

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

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

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

find a general solution using the method of undetermined
coefficients for a given differential equation.
y'=[-3 1; 1 -3]y+[-6 2]e^-2t
Please explain it as easily as possible.
Please write so that I can read your handwriting.

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

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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