Solve
using shift and differential operator .
What does mean?
Continue ?
Can this ODE system be solved?
Is there a method to solve the following ODE system?
with initial conditions .
Application of Rolle's
Suppose q is a nonzero function of a real-variable such that
for all u.
What is the frequency response of a first-order system of ODEs?
What is the frequency response of a first-order system of ODEs? Specifically, given the differential equation:
where y: and , what is the solution when
Essentially, if we have a first-order system of ODEs and we activate a single input with a sine wave of a given frequency, what is the solution? Normally, the frequency response is worked out for a linear time invariant system of higher order and the solution is just a phase shifted and amplitude scaled version of the sine wave. I'm interested in what this result looks like for a first-order system rather than a single equation.
Can 2 different ODE's have the same set of solutions?
If I have two differents linear ODE's:
Coul they have exactly the same set of solutions?
And if we have two different non-linear ODE's could they?
Assessing stability or instability of a system of equations with complex eigenvalues
Having this system , we get clearly two complex eigenvalues. If one has to assess the stability of the system at these eigenvalues, we have for the matrix A:
that , where , while . But with complex eigenvalues , T which must be real, becomes complex and is always 0, when it would vary from greater than or lesser than zero for real eigenvalues. How do we solve this with complex eigenvalues?