Question

4. Find a particular solution, and the general solution to the associated homogeneous equation, of the following differential equations:

a) y'-2y=6

b) y'+y=3e^{-t}

Answer #1

4. Find the general
solution to the homogeneous equation, then use the method of
undetermined coefficients to find the particular solution
y’’− 2y’ + 2y =
360e−t sin3t.

B. a non-homogeneous differential equation, a complementary
solution, and a particular solution are given. Find a solution
satisfying the given initial conditions.
y''-2y'-3y=6 y(0)=3 y'(0) = 11 yc=
C1e-x+C2e3x
yp = -2
C. a third-order homogeneous linear equation and three linearly
independent solutions are given. Find a particular solution
satisfying the given initial conditions
y'''+2y''-y'-2y=0, y(0) =1, y'(0) = 2, y''(0) = 0
y1=ex, y2=e-x,,
y3= e-2x

dy/dt - 2y = 7e^(2t)
a. Determine the general solution to the associated homogeneous
equation.
b. By choosing an appropriate guess, determine a particular
solution to this differential equation.
c. Using your answers from parts (a) and (b), write down the
general solution to the original equation
d. Check that your solution is correct by plugging it into the
original ODE.
e. Determine the specific solution corresponding to the initial
condition y(0)= 3
Pls explain how you did it

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

Find the general solution of each of the following two
homogeneous 2nd order differential equations:
(a) y''' + 4y'' + 4y' = 0
b) y^(4) − 16y'' = 0

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 of the non-homogeneous differential
equation y "+ y = csc² x.

The indicated function y1(x) is a solution of the associated
homogeneous differential equation. Use the method of reduction of
order to find a second solution y2(x) and a particular solution of
the given nonhomoegeneous equation.
y'' − y' = e^x
y1 = e^x

Find the general solution to the differential equation
t^2y'' - 2ty' + 2y = 4

Find the general solution to the non-homogeneous differential
equation.
y'' + 4y' + 3y = 2x2
y(x) =

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