Differential Definition and 1000 Threads

The normalized differential quantum-field-theoretic probability ##dP## of scattering is given by ##dP=\frac{|\langle f |S|i\rangle|^{2}}{\langle f|f\rangle\langle i|i\rangle}d\Pi,## where ##|i\rangle## is the initial state, ##|f\rangle## is the final state, ##\langle f|S|i\rangle## are the...

I'm pretty rusty at calculus. I did well in them, but my memory is terrible and I have forgotten a lot. I'm going to take ordinary differential equations (it looks and sounds like an intro DE class with some linear algebra too) next spring. What should I study and what not to prepare for this...

Homework Statement Solve (x-1)y''-xy'+y=0 , given x>1 and y1=ex Homework EquationsThe Attempt at a Solution I've tried solving it by multiplying everythin for (1/x-1), so my equation looks like: y''-(x/x-1)y'+y=0 (because x-1 is unequal to 0) (1) so now the equation has the...

I would really appreciate if you could help me with a question I have. I was having a debate with someone I work with about whether or not a car with an open diff can spin both wheels at the same time (aka do a burnout). Let me know if my logic is incorrect. If a RWD car is on ice (low friction)...

I have to build a digital peak flow meter. I ve read that you can measure the volume metric flow rate using a differential pressure sensor. H ow do i go about doing so. The peak flow meter will be used to measure asthma.

Homework Statement Solve y''+(cosx)y=0 with power series (centered at 0) Homework Equations y(x) = Σ anxn The Attempt at a Solution I would just like for someone to check my work: I first computed (cosx)y like this: (cosx)y = (1-x2/2!+x4/4!+ ...)*(a0+a1x+a2x2 +...)...

Homework Statement dy/dx = (x+4y)2 Homework EquationsThe Attempt at a Solution I substitute y=ux, where u is a function of x, and I'm not a ble to solve. My intention was to arrive at a seperable form, but I'm not achieving it.[/B]

Homework Statement I'm having difficulty deriving the differential equation, this is what I have so far. In order to solve it, I will be using Matlab, and I'll be using the equation dy/dx ≈ (y(x + dx) - y(x))/dx. Is my derivation correct so far? Homework Equations In picture. The Attempt at a...

Hello! I want to learn about the mathematics of General Relativity, about Topology and Differential Geometry in general. I am looking for a book that has applications in physics. But, most importantly, i want a book that offers geometrical intuition(graphs and illustrations are a huge plus) but...

Homework Statement Given a function g(t)=acosωt + bsinωt, where a and b are constants, show that g(t) is the real part of the complex function: keiΦeiωt for some k and Φ Remark: the complex expression keiΦ is called a phasor. If we know that g(t) has the form kcos(ωt+Φ) then we need know only...

Homework Statement The problem is in the picture. #17 I would have typed it but there are graphs that are needed for solving it. Basically trying to figure out which y(t) graph belongs to one of the sinusoidal forced equations with various parameters. Homework Equations euler's formula...

Homework Statement dx/dt + dy/dt = 2x + 2y + 1 dx/dt + 2(dy/dt) = y + 3 Homework Equations The Attempt at a Solution Dx + Dy = 2x + 2y + 1 Dx + 2Dy = y + 3 --Rearranging---------------------------- Dx - 2x = -Dy + 2y + 1 Dx = -2Dy + y + 3 ---Factoring----------------------------- (D...

Homework Statement The Hamiltonian for a single diatomic molecule of identical atoms is given as $$H=\dfrac{\vec{p_1}\cdot\vec{p_1}}{2m}+\dfrac{\vec{p_2}\cdot\vec{p_2}}{2m}+\dfrac{K}{2}(\vec{r_1}-\vec{r_2})\cdot(\vec{r_1}-\vec{r_2})$$. Find the grand canonical partition function for a gas of...

Hello every one, I have an equation related to my research. I wonder if anyone has any suggestion about solving it? y''+y' f(y)+g(y)=h(x) thanks

I'm practicing for the Physics GRE, and came across a question that has me stumped. "In elementary nuclear physics, we learn about the Fermi gas model of the nucleus. The Fermi energy for normal nuclear density (ρ0) is 38.4 MeV. Suppose that the nucleus is compressed, for example in a heavy ion...

What are some good general textbooks on the properties and solution of systems of partial differential equations? I'm most interested in the general theory of vector and tensor valued PDEs like Maxwell's, Navier-Stokes, and the bulk equations governing elasticity and deformation of solids, etc...

Hi. I'm trying to self-study differential geometry and have come across interior products of vectors and differential forms. I will use brackets to show the interior product and I would just like to check I am understanding something correctly. Do I need to manipulate the differential form to...

Homework Statement Find constants a and b such that y=ax + b is a solution to the differential equation dy/dx = 4x - 2y Homework EquationsThe Attempt at a Solution I already have the solution that is: a=4x-2 (ax+b) (I'm fine with this part) a = (4-2a) x - 2b (what happened here?) 4-2a=0...

Let x(t)= [x1(t) x2(t)] be a solution to the system of differential equations: x′1(t)=−2x1(t)+2x2(t) x′2(t)==−6x1(t)+9x2(t) If x(0)= [4 -2] find x(t). I got the eigenvalues to be -6 and -5, but I don't know how to calculate the coefficients in front of the exponents. For lambda=-6 I get...

Hello. I'm solving the second order nonlinear ODE, and I'm not sure that it's possible or not. Please help. A_0, B_0, C_0, a, b, c, e, p is all known constant. dA/dt = -(a+b*C)*B dB/dt = -p*c*A dC/dt = -(1-p)*e*A then I want to get a solution like A(t) = function of (A_0, B_0, C_0, a, b, c...

Homework Statement Solve the differential equation, dt/dv= 1/g (1/1-a^2*v^2) where a = (k/mg)^1/2 to yield v= 1/a(1-e^-2agt/1+e^-2agt). Homework Equations F=ma Newton's 2nd Law Integration Laws The Attempt at a Solution See image. I think I'm getting messed up on the integration laws.

Homework Statement Solution of the differential equation ##(\cos x )dy = y (\sin x - y) dx , 0 < x < \dfrac{\pi}{2} ## is Homework EquationsThe Attempt at a Solution Only separation of variables, homogenous and linear DEs are in the syllabus, therefore it must be one of those. It obviously...

Mod note: Thread title changed from "Sign used in total differential and small errors" to "Symbol used in total differential and small errors" My notes say that z=f(x,y) can be defined as the sum of the changes with respect to x,y respectively. The formula is: dz = ∂f/∂x * dz + ∂f/∂y * dy...

The figure shows a differential amplifier with a differential input vid = (vin_d_pos - vin_d_neg) between the bases of Q1 and Q2, and an output (out) at the emitter of Q4. I have to Determine R1, R2, R4, R5 and R6 so that the following requirements are met: R 1 = R 2 Av = vout / vid = 100 [V /...

Homework Statement Suppose that f has an inverse and f(-4)=2, f '(-4)=2/5. If G= (1/f-1) what is g '(2) ? If it helps the answer is (-5/32) Homework Equations [/B] f-1'(b)=1/(f')(a) The Attempt at a Solution Im not really sure how to start this problem. I am familiar with how to use the...

In my Halliday Resnick Walker book, they derive the equations of kinematics using integrals in a small section after the algebraic derivation. I'm extremely confused by the calculus, however. Sorry if my questions are unclear.They say that \frac{dx}{dt}=v⇒dx=v\cdot dt. This first step itself...

I obtained an extra factor of ##\frac{1}{l^2}## in the first term on the LHS of (3.34). From (3.33), LHS ##=u^2\frac{d}{d\theta}(\frac{u^2}{m}\frac{du}{d\theta}\frac{dr}{du})-\frac{l^2u^3}{m}## ##=u^2\frac{d}{d\theta}(-\frac{1}{m}\frac{du}{d\theta})-\frac{l^2u^3}{m}##...

Homework Statement dy/dx = (x-y+2) / (x+y-2) , by using x=X and y=Y+2 , form a differential equation . Homework EquationsThe Attempt at a Solution the author gave the answer as (Y^2) +(2XY) -(X^2)+A= 0 , while my answer is (Y^2) +(2XY) -(X^2)+A(X^4)= 0 is there anything wrong with my answer?

y" - 2xy' + my = 0 this is well known hermite diff eqn. now can anyone tell me what kind of conts is m?? what is the suitable value of m??

Homework Statement Consider the linear system: dx/dt=x-y dy/dt=x+3y a. show that the function (x(t), y(t))=(te2t, -(t+1)e2t) is a solution to the differential equation (easy) b. Solve the initial value problem dx/dt=x-y dy/dt=x+3y y(0)=(0,2) need help with part b not a Homework Equations...

Hi I'm just having trouble wrapping my head around differential equations with matrices and vectors... For example: let y be a vector. let A(t) be an nxn matrix. I have the differential equation: dy/dt = A(t)y So I think I understand why the solution is y = ceA(t) But I'm having trouble...

Because on the book it is said that little angles are vectors but my question is: Are they vectors at all or they are scalar and we assign them a direction by multiplying them by a versor? The same for angular velocity, is it a vector at all or we made it a vector for making the right hand rule...

I need to solve the well known momentum equation in 3D cylindrical coordinates: ρ(∂v/∂t +(v.∇)v)=A where A and the velocity v are both local vector variables. I am actually looking for the stationary solution to the equation, i.e. no ∂/∂t term) I have tried evolving the velocity and tried...

Let $\mathbf{A} = \begin{pmatrix} 9 & 2 \\ 1 & 8 \end{pmatrix}.$ Obtain the general solution $\mathbf{y}(t)$ of the system of differential equations $\displaystyle \frac{d\mathbf{y}}{dt} = \mathbf{Ay}$: $\begin{cases} \frac{dy_1}{dt} = 9y_1+2y_2 \\ \frac{dy_2}{dt} = y_1+8y_2 \end{cases}$...

1. Homework Statement A tree is planted as a seedling of negligible height. The rate of increase of its height , in metres per year is given by ##0.2√(25-h)## a. explain why tree can't exceed 25 metres. answer⇒ ##dh/dt=0## when h=25 b. express t as a function of h answer⇒...

Homework Statement I am supposed to write a script that can solve the Schrödinger equation on a nonuniform grid. Homework Equations Finite element approximation to the second derivative as in: https://www.physicsforums.com/threads/nonuniform-finite-element-method.857334/#post-5382329 The...

Homework Statement A boy is eating a 250 gram burger. When he has eaten a mass m grams, his rate of consumption is given by ## 100-1/900m^2## grams per minute. How long does it take him to finish the meal?[/B]Homework EquationsThe Attempt at a Solution ##dm/dt=100-1/900m^2 ...

Hello! How do I solve the following integral and differential equations 1. $x^2f''(x)-2xf'(x) = x$ 2. $\int_0^{x} (1+f(x))\;{dx} = x$ I'm supposed to http://mathhelpboards.com/linear-abstract-algebra-14/linear-subspaces-17957.html all the polynomials that satisfy this, but I can't. (Shake)

Homework Statement Find the general solution to differential equation y''-6y'+9y=e^x((2x+1)\cos x+(x+3)\sin x) Homework Equations -Non homogeneous differential equation -Homogeneous differential equation with constant coefficients -Method of undetermined coefficients The Attempt at a Solution...

Homework Statement my ans is lnx = (-1/y) + c (-1/y) = lnx -c y = -1/ (lnx -c ) , but the answer given is (-1/ln x )+ C , how to get the answer given ? Homework EquationsThe Attempt at a Solution

Homework Statement Find the solution to: $$\frac{d^2}{dt^2} x + \omega^2 x = \delta (t)$$ Given the initial condition that ##x=0## for ##t<0##. First find the general solution to ##t>0## and ##t<0##. Homework Equations The Attempt at a Solution This looks like a non-homogeneous second...

Homework Statement A comet in deep space picks up mass as it travels through a large stationary dust cloud. It is subject to a gravitational force of magnitude Mf acting in the direction of its motion. When it entered the cloud, the comet had mass M and speed V. After a time t, it has traveled...

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 =...

In the first image it shows the ##\alpha^2-w_0^2<0## situation whereas in the second image the situation is when ##\alpha^2-w_0^2=0##.The problem is the book says to use ##T_0=2\pi/w_0## to determine diabetes but you can't do that when ##\alpha^2-w_0^2=0## because it can't be put into a cosine...

Homework Statement Analyse the circuit to provide predictions for (a) the differential input resistance, (b) differential voltage gain, (c) single-ended voltage gain, (d) common-mode voltage gain, (e) common-mode rejection ratio (CMRR) in dB, (f) common-mode input resistance and (g) the...

Are there any known analytical method to solve the equation $$ A\frac{d^2f(x)}{dx^2}+B\frac{df(x)}{dx}+Ce^{igx}f(x) = 0\hspace{1cm}? $$ All quantities appearing in that equation are complex except for ##g## and ##x##.

As it says; I was looking over some provided solutions to a problem set I was given and noticed that, in finding the expectation value for the momentum operator of a given wavefunction, the following (constants/irrelevant stuff taken out) happened in the integrand...

I'm taking an engineering heat transfer course as an elective. 1. Homework Statement Copper tubing is joined to a solar collector plate of thickness t, and the working fluid maintains the temperature of the plate above the tubes at To. There is a uniform net radiation heat flux q”rad to the...

Homework Statement I'm asked to use the transformation of v= 2x-y to solve dy/dx = (2x-y+4)/ (4x-2y +1) the answer given is (2/9)(6x-3y-2) +(7/9)ln(6x-3y-2) = x +c , i got (2/9)(6x-3y) +(7/9)ln(6x-3y-2) = x +c , what's wrong with my working ? Homework EquationsThe Attempt at a Solution

Greetings all, In my quest to imagine the ultimate sportscar, I began to wonder about the following: Certain cars are All Wheel Driven (AWD) and they do so via a Center differential delivering power to both axles. Amongst those cars, some have fixed Torque Bias/Split Ratio, which doesn't alter...