Question

give an example of linear system of differential equations with
constant coefficients. thanks

Answer #1

1. Give an example of a linear system of two equations
with two unknowns. Also give an example of a linear system of three
equations with three unknowns.
2. What are the two properties that define an echelon
matrix? What are the additional two properties needed to define a
reduced echelon matrix? Give an example of a reduced echelon
matrix, and give an example of an echelon matrix that is not
reduced.

Write the second order differential equation as a system of two
linear differential equations then solve it.
x''-6x'+13x=0 x(0)= -1 x'(0)=1

What are some situations that can be modeled by a system of
linear differential equations? Why do they need a system as opposed
to a single equation?

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

What is the difference between qualitative and quantitative
techniques in differential equations. Give an example of
both.

Is the following statement true or false: If a system of two linear differential equations is saddle point stable, the variables can move against their steady state values over time. Explain your answer.

Write down a homogeneous second-order linear differential
equation with constant coefficients whose solutions are:
a. e^-xcos(x) , e^-xsin(x)
b. x , e^x

find a homogeneous linear differential equation with constant
coefficients whose general solution is given:
c1e^(x)sin4x+c2e^(x)cos4x

Find a particular solution to the given linear system of
differential equations:
dx1/dt = 4x1 + 5x2
dx2/dt = x1 + 8x2
, with initial conditions x1(0) = 6, and
x2(0) = 0.

Find the solution to the linear system of differential
equations
{x′ = 6x + 4y
{y′=−2x
satisfying the initial conditions x(0)=−5 and
y(0)=−4.
x(t) = _____
y(t) = _____

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