What is Second order: Definition and 602 Discussions
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory.
First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence
∀
P
∀
x
(
P
x
∨
¬
P
x
)
{\displaystyle \forall P\,\forall x(Px\lor \neg Px)}
says that for every formula P, and every individual x, either Px is true or not(Px) is true (this is the law of excluded middle). Second-order logic also includes quantification over sets, functions, and other variables as explained in the section Syntax and fragments. Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.
Second Order RLC CIrcuit?
Homework Statement
for this figure, vin(t) = -250u(-t) + 750U(t) mV, R = 0.5 ohms, L = 1 H, C = 0.01 F.
Find zero-input, zero state, and complete response of both Vc(t) and IL(t) for t>0.
Homework Equations
?
The Attempt at a Solution
I found the iL...
Homework Statement
find the general solution to the ODE:
y''+(1/x)y'=0
Homework Equations
The Attempt at a Solution
I put this in the following form: y''=-(1/x)y'
integrated both sides: y'=-ln(x)y +C
I think i made a stupid mistake but i can't figure out what it is.
Any help...
Homework Statement
if z= f(x) + yg(x), what can you say about zyy explain?
Homework Equations
The Attempt at a Solution
z= f(x,yy)
zyy = d/dy (dz/dy) d(partial derivative)
Homework Statement
Find the general solution of the following diff. eqn.
y''(t) + 4y'(t) + 4y(t) = t^(-2)*e^(-2t) where t>0
Homework Equations
General soln - Φgeneral(t) + Φparticular(t)
Wronskian - Φ1(t)Φ22'(t) - Φ2(t)Φ1'(t)
The Attempt at a Solution
I'm solving by...
Homework Statement
Find all values of a for which all solutions of
y''(x) + (a/x)y'(x) + (5/2)y(x) = 0
tend to zero as x tends 0+ and all values for which all solutions tend to zero as x tends to +
Homework Equations
The Attempt at a Solution
I am not even sure where to being with this...
second order ODE solution for this system??
hello guys,
I am wondering if what is the analytical solution for this system?
can we solve it as a mass-spring-damper system?
thanks for your helps.
the rectangular part is removed from the disk.
http://img3.imageshack.us/img3/3610/odev.th.jpg
I know there are many ways to identify the spectra but,
what are the advantages and disadvantages of using the first and second order lines to identify spectra?
Please Help!
If u don't want give me answer then suggest me some links.
Thanks
Homework Statement
The following contour diagram represents the function z = f(x,y)
http://img15.imageshack.us/img15/9059/contour.th.jpg
(a) Is z an increasing or decreasing function of x?
I'd say it's increasing as it goes towards the x-axis the contour lines value goes down
(b) Is z...
could anyone help me with solving this second order differential equation? I am a noob on here so not sure how you get the mathplayer stuff on... so the equation is of the form
x'' +ax' + bx^n = 0
(x^n means x to the power n, with a and b constants). i tried substituting x'=u to get a first...
Little homework problem that I'm beating myself up over...
Solve:
xy'' - 2y' + xy = -2\cos x
Using the method of Laplace transforms...
So I do some jiggling and get to:
(1+s^{2})\frac{dF}{ds}+4sF(s) = \frac{2s}{s^{2} + 1}
To which I find the following solution:
F(s) =...
Hi all,
My maths are very rusty and I would need some advice. I have some experimental results obtained in an open channel and got depth-averaged velocity u(y) at different cross-sectional locations y. I tried different models but there is one I don't know how to tackle. The following one...
Dear all,
Im trying to solve the following ode:
y'' = -0.12*y + 0.4/sqrt(y^2 + 5.76) , y=y(t) , t: [-50,50]
y(-50)=2.3 , y'(-50)=0
i changed it to a set of two first order ode using z=y'
and solve it with finite differences.
note that the right side...
Hi,
I'm having problems solving this equation;
y'' -2y' +3y =0 y(0)=-1 , y'(0)=(root 2) -1
I found the auxiliary equation r^2 -2r +3 = 0
and since b^2 -4ac is less than zero this the case where r1 and r2 are complex numbers.
This is as far as I get without getting stuck...
Hey guys,
I have a question about the Bode diagram of a second order high-pass filter (one with both a capacitance and an inductance). The Bode-diagram of the amplitude looks like this.
http://dave.uta.edu/dillon/pspice/images/pst07g.jpg
Here, the cutoff frequency is equal to about 10 kHz...
hi,
i am facing problem in solving the following differential equation. help me.
y''+ayy'+b=0, where y is a function of x, 'a' & 'b' are constants.
i have tried substituting y'=u, which implies u'=u*dy/dx, these substitution change the equation to first order but i found no...
1. Homework Statement + relevant equations
I have to solve
http://home.vs.moe.edu.sg/linl/eqn1.gif
sigma, pinfinity, rho, N are constants. To make things easier for us, we are allowed to treat T as a constant.
2. The attempt at a solution
Treat T as constant...
Hi
In my lecturer's notes he describes the unit tangent to a curve y=Y(X) as
(i + Y'(X)j)/[(1+[Y'(X)]^2)^(0.5)]
in an introduction to second order PDEs
I'm a bit confused by this. Where did it come from?
Can anyone explain
Thanks
Homework Statement
Write a function and solver for the chaotic motion of stars in a galaxy
Initial conditions:
x at time zero = 0
velocity of x at time zero = 0.3
y at time zero = 0
velocity of y at time zero = 0
Time period 2 to 200 with an interval od 0.02
Homework Equations...
Hello and thanks to all who read this.
I'm trying to teach myself applied mathematics, specifically (simple) differential equations.
I've been solving them all fine, so far, but now I've come across second order DE's with a squared term, and I can't seem to get the right answer. I'll give...
Homework Statement
I am modeling a set of equations for a protein network. It is a feedback loop between 2 proteins. I have gotten the differential equations for this model and plan on doing an extended Kalman Filter to estimate the levels of protein in real time. However, I am having...
Does anyone know how to solve the following Non-linear, second order, differential equation?
A*y" + B*(y')^2 = F(t) + C
where A, B, & C are constants
**please note, in case the above notation isn't clear, the y' term is squared which is what makes it non-linear. Also, F(t) is time...
I would very much appreciate if anyone can help me with this problem; I have approached it from many different angles to no avail.
The position x(t) of a particle moving along the x-axis is governed by the differential
equation:
x'' + kx' + (n^2)x = 0 , and initially x(0) = a, x'(0) = u...
Homework Statement
Find the terms up to x^5 in the power series solution of the following equation
y''=(1+x^{2})y
Homework Equations
Power series, sum from 0 to infinity
y=\sum a_{n}x^{n}
The Attempt at a Solution
At first I just differentiated each term separately and...
Homework Statement
I've completed this question but I don't think I've got it right. It's from a 2008 June FP1 further maths paper. There is a second part to the question I don't understand which I will post after I know I have got this part right :)
Find, in terms of k, the general...
Homework Statement
A projectile is fired with an initial speed of 1000 m/s at an angle α from the horizontal. A
good model for the path uses an air-resistance force proportional to the square of the speed.
This leads to the following equations for the acceleration in the x and y directions...
This is the question word for word:
a) Solve the initial value problem: x'' + x = 2cos(\omega t) ; x(0) = 0 ; x'(0) = 0 ; \omega != 1
b) repeat but with \omega = 1
c) use the trigonometric identity: cos(\alpha) - cos(\beta) = -2sin(\frac{\alpha + \beta}{2})sin(\frac{\alpha - \beta}{2})...
Homework Statement
A 2-\mu F capacitor is charged to 20 V and then connected across a 6-\mu H inductor forming an LC circuit.
(a) Find the initial charge on the capacitor
(b) At the time of connection, the initial current is zero. Assuming no resistance, find the amplitude, frequency and...
The Problem
You are given: http://img530.imageshack.us/img530/4468/88346476ca9.jpg
Where http://img408.imageshack.us/img408/209/53113174nt5.jpg is constant (taken as B).
a) Differentiate both sides to produce a second order ODE for y(x)
b) Show that it can be written as a first order ODE...
Homework Statement
Hi
I need to solve the following:
\frac{d^{2} x}{dt} + 2 b \frac{dx}{dt} + (b^2 - \frac{db}{dt}) x = 0[/tex]
2. The attempt at a solution
Isn't this equivalent to??::
[itex]x^{''} + 2bx^{'}+ (b^2 - b^{'})x = 0 \iff x^2 + 2x +1 = 0 If I let b = 1.
which...
Hi everyone. I am really confused at the moment learning about Second Order homogeneous linear differential equations. I lay out the background of what I would like to understand. So I understand the actual maths that goes into the diff's, but I do not understand why it should be so, given the...
ive been doing Xdot and Ydot questions using the formula lamda2-(a+d)lamda +ad-bc=0 where Xdot=ax+bc and ydot=cx+dy no problems so far until this question where i have the second order equation xdot dot+x-1/4x3=0
so i set Xdot dot =Ydot and therefore Xdot =y as usual but this gives me...
Homework Statement
A 32 pound weight stretches 2 feet. Determine the amplitude and period of motion if the weight is released 1 foot above the equilibrium position with an initial velocity of 2 ft/s upward. How many complete vibrations will the weight have completed at the end of 4 pi seconds...
Homework Statement
I have no idea about how to solve the second order differential equation. Please someone help me solve this. Or provie me some articles for beginnrs. I have only basic knowldge of calculus.
While solving a question at physics, I got this...
Hey guys.
I need to know how to draw a Phase Bode plot of a Second order system.
I understand and can draw the Gain(Magnitude) Bode plot, but I can't seem to get the grip of the Phase one.
As far as I know there is an asymptote at 0^{o} at low frequencies and an asymptote at 180^{o} at...
I just finished a final in my differential equations class. One of the problems had me solve a second order homogeneous differential equation using series. I boiled it down to this recursion relation:
a_{n+2}=\frac{(n+3)a_{n}}{2(n+2)(n+1)}
I found that the even coefficients work out...
Hey; not much of a homework question, but something i was wanting to find out.
Im still a first year undergraduate and just started on differential equations. We have just finished going over homogeneous 2nd order ODE's of the form:
ay'' + by' + cy = 0
My texbook briefly outlines the...
hey I am having a little trouble with this topic. Here are the questions I was set.
a) Find the general solution of d^2y/dt^2 - 2(dy/dt) + y = 0. Verify your answer.
b) Solve the initial value problem y'' + 4y' + 5y = 0; y(0)= -3, y'(0) = 0
c) Find a DE that has the given functions as...
Hello. I am an engineering student and am having trouble trying to figure out how to solve this system of second order, nonhomogeneous equations. I know how to solve a single second order, nonhomo. equation and how to solve a system of first orders, but not this one. Any help would be greatly...
Homework Statement
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an externam...
Homework Statement
a) Show that phi(t) = e^2t is a solution of y' - 2y = 0 and that C*phi(t) is also a solution for any constant C
b) Show that phi(t) = 1/t is a solution of y' + y^2 = 0 for t>0 but that y = c*phi(t) is not a solution unless c = 0 or c = 1
Homework Equations
What do...
y'' - 8y' + 16 = 0 ; y(0) = 4 ; y'(0) = 9
this should be not too bad but I am stuck in the same place.
m^2 - 8m + 16
m1 = m2 = 4
y = C1e^(mx) + C2(e^(mx))
sub in y(0) = 4
4 = C1 + C2
C1 = 4-C2
y' = mC1e^(mx) + mC2e^(mx)
sub in y'(0) = 9
9 = mC1 + mC2
C1 = 4 - C2...
Hi, I am trying to decide whether y(t) = c1t^2 + c2 t^−1, where c1 and c2 are arbitrary constants, is the general solution of the differential equation (t^2)y'' − 2y = 0 for t > 0 and justify the answer, but I don't really know how to approach it from this "side" of the problem.
Any suggestions...
It's been a while since I've had DE, and it seems I have forgotten something basic, yet crucial. In solving the Time-Independent Schrodinger Wave Equation in one dimension, I have the following:
\left( -\frac{\hbar}{2m} \frac{\partial^2}{\partial x^2}+V\right) \Psi(x)=E\Psi(X)...
Homework Statement
I have two questions:
1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1)
2)I have two second order ODES X''=... and Z''=... to solve this, we make the...
[SOLVED] Nonhomogenous Second Order DE
Homework Statement
y'' - 2y' - 3y = -3te^{-t}
SolveHomework Equations
The Attempt at a Solution
Well first I tried
Y(t) = Ate^{-t}
then
Y(t) = At^2e^{-t}
then
Y(t) = At^3e^{-t}
and
Y(t) = At^3e^{-t} + Bt^2e^{-t}
but I can't seem to get the correct...
Hi every one !
I am a final year Engineering student of IIT Madras, India. I am doing a project(finite element analysis of a structure) which requires the solution of a system of second order differential equations. equation looks like below:
[M][U"]+K[U]=[F(t)]
M : Mass Matrix of size...