Question

suppose that the characteristic equation of third order differential has roots +-2i and 3

i) What is the characteristic equation?

ii) find the corresponding Differential equation?

iii) Find the general solution?

Answer #1

In exercises 7-12, given the list of roots and multiplicities of
the characteristic equation, form a general solution. What is the
order of the corresponding differential equation?
r = -2, k = 3; r = 2, k = 1
Answer is apparently 4th order,
y=(c1+c2t+c3t^(2))e^(-2t)+c4e^(2t)

Give the general solution to the differential equation that has the
roots m= 1,1,-5, 2 +or- 3i

For the below ordinary differential equation, state the order
and determine if the equation is linear or nonlinear. Then find the
general solution of the ordinary differential equation. Verify your
solution.
x dy/dx+y=xsin(x)
Please no handwriting unless I can read it.

Consider the following second-order differential equation:
?"(?)−?′(?)−6?(?)=?(?)
(1) Let ?(?)=−12e^t. Find the general solution to the above
equation.
(2) Let ?(?)=−12.
a) Convert the above second-order differential equation into a
system of first-order differential equations.
b) For your system of first-order differential equations in part
a), find the characteristic equation, eigenvalues and their
associated eigenvectors.
c) Find the equilibrium for your system of first-order
differential equations. Draw a phase diagram to illustrate the
stability property of the equilibrium.

Consider the differential equation: y'' = y' + y
a) derive the characteristic polynomial for the differential
equation
b) write the general form of the solution to the differential
equation
c) using the general solution, solve the initial value problem:
y(0) = 0, y'(0) = 1
d) Using only the information provided in the description of the
initial value problem, make an educated guess as to what the value
of y''(0) is and explain how you made your guess

Consider the differential equation x^2y′′ − 3xy′ − 5y = 0. Note
that this is not a constant coefficient differential equation, but
it is linear. The theory of linear differential equations states
that the dimension of the space of all homogeneous solutions equals
the order of the differential equation, so that a fundamental
solution set for this equation should have two linearly fundamental
solutions.
• Assume that y = x^r is a solution. Find the resulting
characteristic equation for r....

1. The forced response for a first-order differential equation
with a constant forcing function is also referred to as the
steady-state solution.
True or false
2. If the roots of the characteristic equation for a
second-order circuit are real and equal, the network response
is:
a. overdamped
b. underdamped
c. critically damped
3. If the response of a second-order circuit is oscillatory, the
circuit is
a. underdamped
b. critically damped
c. overdamped
4. The forced response for a second-order circuit...

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

Use the METHOD of REDUCTION OF ORDER to find the general
solution of the differential equation y"-4y=2 given that y1=e^-2x
is a solution for the associated differential equation. When
solving, use y=y1u and w=u'.

Find the General Solution of the Differential Equation (y' =
dy/dx) of
xy' = 6y+9x5*y2/3
I understand this is done with Bernoullis Equation but I can't seem
to algebraically understand this.

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