Question

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

Answer #1

Find the general solution of the given higher order differential
equation
y^(4) + 4y^(3) − 4y^(2) − 16y^(1) = 0
Derivatives of Y not power

1. Find the general solution of each of the following
differential equations a.) y' − 4y = e^(2x) b.) dy/dx = 1/[x(y −
1)] c.) 2y'' − 5y' − 3y = 0

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

(a) Solve the differential equations.
4y´´ + 12y´ + 9y= 0
(b) Find the general solution of the ODE
y´´- 5y´+4y=e^4t
(c) Solve the following initial value problem:
y´´+ y =0, y(0)=2, y´(0)=2

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

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

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.

4. For each of the following equations find the general
solution.
(a) y" + 2y' + 2y = etsin(t)
(b) y(4) - 4y" + 4y = et -
te2t

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

Question 11:
What is the general solution of the following homogeneous
second-order differential equation?
d^2y/dx^2 + 10 dy/dx + 25.y =0
(a)
y = e 12.5.x (Ax + B)
(b)
y = e -5.x (Ax + B)
(c)
y = e -10.x (Ax + B)
(d)
y = e +5.x (Ax + B)
Question 12:
What is the general solution of the following homogeneous
second-order differential equation?
Non-integers are expressed to one decimal place.
d^2y/dx^2 − 38.y =0
(a)
y...

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