Differential Definition and 1000 Threads

I have the following linear differential equations: ##A\dot{x} + By = 0## ##C\dot{y} + Dx = 0## Where x and y are functions of t, and A through D are constants. I can solve this fairly easily by differentiating the first equation, rearranging, and removing one of the variables, which gives me a...

Homework Statement The equation of motion of a particle is given by the differential equation ##\frac{d^2x}{dt^2} = -kx##, where ##x## is the displacement of the particle from the origin at time ##t##, and ##k## is a positive constant. 1. Show that ##x = A\cos{(kt)}+B\sin{(kt)}##, where ##A##...

Homework Statement [/B] (dy/dx)^2 = (1-y^2) / (1-x^2)Homework Equations Separating the variables I arrive with: dy/sqrt(1-y^2) = dx/sqrt(1-x^2) By integration on both sides by trigonometric substitution and putting it in a general solution: Arcsin y - Arcsin x = C The Attempt at a Solution If...

I have been stuck in this problem for two days now. I am starting DE this semester and I want to move ahead. so for this problem I attempted to use x=yv, then v=x/y. so I move dy/dx to the other side of the equation and divide by 2xy both sides, which leads to (3x^2-2y^2)/(2xy)=dx/dy. then...

Hi I understood above differential ## typo. RHS= 2*f ' (x,2z-x) but, what is answer of below equation? is this right? f ' ( g(z),2z-x) * g' (z) + f ' ( g(z),2z-x) *2

Homework Statement Let be E a normded vectoriel space, ##dim(E) = m \in \mathbb{N}^{*}##, I have to show that ##\exists \rho_{1}, \rho_{2} > 0 | \forall u \in L(E), ||u^{m} - Id| \leq \rho_{1} \Rightarrow |u - Id| \leq \rho_{2}##. Homework Equations Nothing. The Attempt at a Solution [/B] I...

Hello folks, Let me explain this. Much effort, time, methods and books is devoted to the science of finding solutions of differential equations. But I cannot find anywhere the reverse problem. Basically I am thinking about the work that Maxwell did finding the differential equations that...

Homework Statement Homework EquationsThe Attempt at a Solution

Homework Statement Why do we need two solutions to solve a 2nd order linear differential equation? lets consider a differential equation with equal roots for auxiliary equation. So the reasoning behind why can't we use y=Aen1x+Ben2x as its general solution is because since the roots are equal...

Let us suppose that we are modeling a particle traversing some distance in space & that f(x)=x². Let the x-axis be time (hrs) & the y-axis be position in space (miles). What is the instantaneous velocity of said particle at t=4 hours? Let's assign variables to each coordinate in our x, y...

[Mentor's note: This question was split off from: https://www.physicsforums.com/threads/meaning-of-physical-quantities-and-division.880214/] What does this differential "d" mean? Why say dE instead of E? or

Hi, there is a book of dg of surfaces that is also about tensor calculus ? Currently i study with Do Carmo, but i am looking for a text that there is also the tensor calculus! Thank you in advance

Hi, I was wondering if anyone had some advice on how to solve the following equation for ## F(b)##: $$ F(g(b)) h(b) + F'(b) s(b) - F(b)h(b) + h(b) + \int_{g(b)}^{b} v(x) F'(x) dx = 0 $$ Any hints on how to tackle this would be highly appreciated. Thank you!

what is a good book to learn first order differential equations ??

what is a good book to learn first order differential equations ??

Hi guys, I'm thinking of maybe of studying differential geometry as part of my undergraduate degree. However, it's not for physicists, it's a full on formal mathematics course specifically for mathematicians. I'm not sure whether it's a bit overkill and won't actually be useful. We don't have a...

i have few doubts about differential equations and numerical methods ... in a differential equation question ... you are given an instantaneous rate of change... and you are supposed to find the function that gives , this instantaneous rate of change is this same as ... f(0)=1...

Homework Statement A health club is opened, the fraction of members still enrolled t months from their initial visit is given by the function f(t)= e-t/20. the club initially accepts 300 members and will accept new members at a rate of 10 per month. How many people will be enrolled 15 months...

Hello guys! I'm new here, so sorry if I'm posting on wrong place or wrong way. I just need help to solve a problem: (∂E/∂V)β, N + β(∂p/∂β)N, V = - p PS: There is a bar over E and over p (this in both sides) - meaning that is an average. I don't know how to start, so any help will be amazing...

Hello, I would like to know if anybody here has used the book "Differential Forms and the Geometry of General Relativity" by Tevian Dray and how they found it. Thanks!

Given a system of linear differential equations $$x_{1}'=a_{11}x_{1}+a_{12}x_{2}+\cdots a_{1n}x_{n}\\ x_{2}'=a_{21}x_{1}+a_{22}x_{2}+\cdots a_{2n}x_{n}\\ \ldots\\ x_{n}'= a_{n1}x_{1}+a_{n2}x_{2}+\cdots a_{nn}x_{n}$$ this can be rewritten in the form of a matrix equation...

Homework Statement Solve ##{dy/dx}-2xy=2x##Homework EquationsThe Attempt at a Solution Let ##P= -2x ## and Q= 2x, Integrating factor =## e^{-x^2} ## ##y.e^{-x^2} = ∫ 2x.e^{-x^2} dx## ##y.e^{-x^2}={x^2} e^{-x^2}+∫ 2{x^3} e^{-x^2}dx## since ##y.e^{-x^2} = ∫ 2x.e^{-x^2} dx## then...

i was trying to learn differential equations ... i was lucky enough to find some good explanations for calculus and differential equations ... Mod note: unrelated image now deleted differential equations in this equation which is the dependent variables and which one is the independent...

I am having trouble to where to put the arbitrary constant in solving order differential equations. Because sometimes when I am solving, I can't really where to put the arbitrary constant if it is either the left side or right side. I am only at equations of order one. Plss keep it simple...

please , I'm french , so i didn't quite get the meaning of this sentence.

Hello I'm doing some problems in QM scattering regarding the Green's function. Homework Statement Determine the differential equation of G(\vec{r},\vec{r}',\omega) Homework Equations I've been given the Fourier transform for the case where the Hamiltonian is time independent...

Homework Statement Calculating the open loop output Impedance at 1kHz and the open loop differential gain The Attempt at a Solution Here is the approach. INPUT STAGE: Q111 and Q112 Av1 = Rtot/2re, where Rtot is the total resistance of R117 and the input resistance of Q78 which is Rin. So...

So I ran into an case I have not seen before. Say we have a system of 3 equations such that W´=AW, where W=(x(t),y(t),z(t)) and A is a 3x3 matrix. The way I usually approach these is by finding the eigenvalues of A to then find the eigenvectors and thus find the ¨homogenous¨ solution. What...

Homework Statement [/B] Solve the differential equation Homework EquationsThe Attempt at a Solution [/B] I just can't integrate that (1+y)^(1/2)/(1+y^2)dy at the end... the other two integrals are trivial.

Hi, This is probably an easy answer but I can't get my head round it! If I have a test rig that measures pressure differential in a test chamber at a set flow rate, how do I calculate what the pressure differential should be if I put an orfice plate in with a certain size diameter hole in the...

Hi members, Laplace transform using differential equations.(see attached PDF file) My question d/ds(s^2 y- s Y(0)-Y'(0).)... Y(t)=sin(sqrt(t)) Y(o)=0 Now Y'= cos(sqrt(t)/2sqrt(t) Y'(0)=infinity d/ds (Y'(0)=?? can it be treated as a constant or can we change limit and differentiation??I...

Hello everyone, I've 2 books on manifolds theory in e-form: 1) Spivack, calculus on manifold 2) Munkres, analysis on manifold What would be good to begin with? :oldconfused: Thank you in advance

I can's understand the fact about the equation i can't prove the equation from the first attachment to the second attachment pls help. Sorry for bad english

I want to use a differential amplifier to separate the digital and analog ground portions of a circuit, but am not confident in my understanding of the datasheet of the amps I have on hand (amp03). http://www.analog.com/media/en/technical-documentation/data-sheets/AMP03.pdf I think that...

Homework Statement Homework EquationsThe Attempt at a Solution So the general solution is the sum of the null solution (Yn) and particular solution (Yp) I believe I just need to write: y = e2t + 5e8t - 5 + C and then find the derivative of both sides y' = 2e2t + 40e8t is this correct?

I’ve been told that “differential aging” and “time dilation” are two different things. I had thought that one was the integral of the other. Can anyone give a PRECISE (mathematical!) definition of each, what the distinctions are between them? Thanks. (How the heck am I supposed to know what...

i have a few questions to ask about differential equations ... how many types of differential equations are there ... ? sometimes i like to make up themes for my studies ... few funny things went through my head ...when i saw this thread ,How is it that mathematics describe reality so well? i...

I want to mount open differential (chain driven) on SAE-INDIA supra -car so I need to consider different forces on differential and it's mounting for designing a proper mounting. So i need physics forum's help to design differential mounting. Mounting place is a box type frame. For illustrative...

Homework Statement The data given was the acceleration of the component over time, as below: time | Acceleration (m/s²) 0 | 0 0,2 |3,61 0,4 |4,5 0,6 |5,4 0,8 |7,508 1 |12 - The Rigidity constat is 12600000 [N/m] (for the spring) The damping constant is 6500 [N/m] (for the damp)...

Homework Statement You have two parameters x = 12 and y = 3 set on a machine. The machine generates a function: z (x, y) = 3sin (x ^ 2 + y) y + x ^ 3 Use the total differential of this function in the set point to determine which of the parameters to be set to the most accurate. Homework...

Homework Statement Calculate d (x * y ^ 4) if x = 2, y = 3, dx and dy = 0.02 = -0.03 Homework Equations Total differentialThe Attempt at a Solution product rule: d(xy^4) = d/dx (xy^4) dx + d/dy (xy^4) dy d(xy^4) = y^4 dx + 4xy^3 dy When x = 2, y = 3, dx = 0.02, y = −0.03 d(xy^4) = (3)^4...

Homework Statement Solve and obtain an expression for x in terms of θ given ## (3+ cos 2θ) dx/dθ = x sin 2θ## Homework EquationsThe Attempt at a Solution ...##dx/x = ((sin 2θ)/(3+ cos 2θ))dθ## , let ##u = (3+cos 2θ)⇒ du/dθ= -2 sin 2θ## thus ##∫dx/x = -1/2∫du/u ##...[/B]are my steps...

I've always wondered what happens when you divide a first order seperable DE by a differential? Does it then become a PDE? Is it still possible to solve it? If so how would one solve such a DE? For example this: Starting with this equation for pressure: ##P=ρgh## ; ## h = -y## ##P= -ρgy##...

Homework Statement Find a solution of $$\frac{1}{x^2}\frac{\partial u(x,y)}{\partial x}+\frac{1}{y^3}\frac{\partial u(x,y)}{\partial y}=0$$ Which satisfies the condition ##\frac{\partial u(x,y)}{\partial x}\big |_{y=0}=x^3## for all ##x##. The Attempt at a Solution I get the following...

Homework Statement Get the two stationary points for the equation ## y= ((ln x)^2)/x ## Homework EquationsThe Attempt at a Solution i have managed to solve ##dy/dx=((2xlnx/x- (ln x)^2))/x^2 = 0, ln x(2-ln x) = 0, x= 1, x =e^2##

I took differential equation 2 last semester and the book we used wasn't so great at explaining a lot of things. I was wondering if anyone knew of a video lecture series that parallels my book (Differential Equations 4th Ed. by Blanchard, Devaney, and Hall). Specifically I am having trouble with...

Hello I have a query regarding how this diffrential pressure sensor works http://www.mouser.com/ds/2/302/MP3V5010-783555.pdf I have used the formula they suggested and I am getting a negative pressure output. I am unable to interpret the reason to such an output, It would be great if someone...

In elementary calculus (and often in courses beyond) we are taught that a differential of a function, ##df## quantifies an infinitesimal change in that function. However, the notion of an infinitesimal is not well-defined and is nonsensical (I mean, one cannot define it in terms of a limit, and...

I am studying a dichotomous markov process. The master equation is given in this link https://en.wikipedia.org/wiki/Telegraph_process. I want to calculate the mean and correlation function given also in the link. But actually I can't make any progress. How from this master equation governing the...

Hi, I am trying to learn about different types of corrosion. I have read that iron can undergo differential aeration corrosion, but not zinc and aluminium. I do not see why...both can be reduced by oxygen and both have a passive film. Can somebody explain why? Thanks