Question

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.

Answer #1

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

Second-Order Linear Non-homogeneous with Constant Coefficients:
Find the general solution to the following differential equation,
using the Method of Undetermined Coefficients.
y''− 2y' + y = 4x + xe^x

Solve the second-order linear differential equation
y′′ − 2y′ − 3y = −32e−x using the method of variation of
parameters.

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

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.)

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 )

use the method of undetermined coefficients to solve the
differential equation)
y'' + 2y' - 3y = (x2 + x + 1) + e-3x

Solve the following differential equations by using variation of
parameters.
y''-y'-2y=e3x

Find the general solution of y'' − 2y' = sin(5x) using the
method of undetermined coefficients

3. Find the general solution to each of the following
differential equations.
(a) y'' - 3y' + 2y = 0
(b) y'' - 10y' = 0
(c) y'' + y' - y = 0
(d) y'' + 2y' + y = 0

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