particular solution Definition and Topics - 7 Discussions
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.
ASSUMPTIONS:
BIBO/stable systems
NOTE: zero here does not mean the roots of the denominator in a transfer function
TRUE/FALSE -Please provide feedback- some answers are based on ODE example listed below
1/True) The Homogenous Solution is either zero or transient.; i.e. it can never be steady...
CONCEPTUAL QUESTIONS:
-Does the Homogenous Solution represent the Transient Response?
Let me specify. For a N-DOF spring, mass, and damper mechanical system:
-Does the Homogenous Solution represent the Transient Response for given mechanical system?
MY ANSWER:
Yes.
ASSUMPTIONS:
-only...
Homework Statement
Particular solution of
y" - y' - 2y = e^(2x)
Homework Equations
None
The Attempt at a Solution
This makes no sense to me, why do I have to use the solution of the form
y(t) = cxe^(2x)
For the problem above, but when I switch the signs and it becomes
y" - y' + 2y =...
imgur link: http://i.imgur.com/8TOXi9t.png
I am comfortable with the need to multiply the polynomial in front of e^{2x} by x^3, that makes perfect sense in terms of what the text has already said about how no term in the particular solution should duplicate a term in the complementary solution...
Homework Statement
Solve: A*sin(ωt + Θ) = L*i''(t) + R*i'(t) + (1/C)*i(t). Where: A=2, L = 1, R=4, 1/C = 3 and Θ=45°.
Homework Equations
The system has to be solved by i(t) = ih + ip. I gave the values to A, L, R, 1/C and Θ. I can also give values to ω, but I've come to a doubt when solving...
Hello,
I noticed that the solution of a homogeneous linear second order DE can be interpreted as the kernel of a linear transformation.
It can also be easily shown that the general solution, Ygeneral, of a nonhomogenous DE is given by:
Ygeneral = Yhomogeneous + Yparticular
My question: Is it...
Hi,
I'll give some background, say you've got a planar structure of thickness 'd', lying on the z plane. Also say the upper and lower surfaces are y = 0 and y = -d, respectively.
The structure has scalar potentials inside it as so:
As you can see the vector fields cancel out on one side, As it...