Differential Definition and 1000 Threads

Homework Statement dNa/dt = -Na/Ta where Na is the function and Ta is the constant dNb/dt = Na/Ta - Nb/Tb where Nb is the function and Tb is the constant Homework Equations My Prof said Nb(t) has the form Nb(t) = Cexp(-t/Ta) + Dexp(-t/Tb) The Attempt at a Solution I know the first equation...

Dear all I am studying general relativity and i have a question as follow. We have the 2- sphere can be scanned totally by a coordinate system (theta, phi) with the metric tensor written in terms of theta and phi. Now i want to divide the 2-sphere into charts 4 charts then each will have its own...

Homework Statement Hello everyone, I need to find K for the following differential equation to be exact. (y3+kxy4-2*x)dx +(3xy2 +20x2y3)dy=0 Homework EquationsThe Attempt at a Solution (y3+kxy4-2*x)dx +(3xy2 +20x2y3)dy=0 dM/dy = d/dy(y3+kxy4-2*x) = 4*k*y3*x+3*y2 dN/dx =d/dx(3xy2 +20x2y3) =...

Homework Statement I need to resolve this with v = y/x dy/dx= (3y2-x2)/(2xy) Homework EquationsThe Attempt at a Solution dy/dx= (3y2-x2)/(2xy) dy/dx= 3y2/2xy -x2/2xy dy/dx = 3y/2x -x/2y dy/dx = 3y/2x - 1/2y/x dy/dx = 3/2 *v - 1/2*v F(v) = 3/2 *v - 1/2*v is that good so far ?

Homework Statement Homework Equations F=ma ac=v^2/r f=uN v=v0+at w=v/r The Attempt at a Solution v=v0+at v=vo+umv^2/r v^2(u/r)-v+vo=0 I don't see what differential equation i could use since the speed is dependent on the friction (equal to friction coeff times centripetal force) which in...

Hi guys, I was browsing in regards to differential equations, the non-linear de and came up with this site in facebook: https://www.facebook.com/nonlinearDE Are these people for real? Can just solve any DE like that, come up with a series? Not an expert in this area, so I do not know what if...

Homework Statement Observe a Cauchy problem \begin{cases}y' + p(x)y =q(x)y^n\\ y(x_0) = y_0\end{cases} Assume ##p(x), q(x)## are continuous for some ##(a,b)\subseteq\mathbb{R}## Verify the equation has a solution and determine the condition for there to be exactly one solution. Homework...

Homework Statement http://imgur.com/goozE9f Homework Equations ##(dx_i)_p i= 1,2,3## 3. The Attempt at a Solution [/B] I'm reading Manfredo and Do Carmo's Differential Forms and Applications. This is the very first page Would you mind explaining me what is meant by dx, as highlighted in the...

I don't know if this is a silly question? Am I missing simple math? How does a wave depending on amplitude and frequency make it's equation a second order differential equation?

I'm trying to understand how the integral form is derived from the differential form of Gauss' law. I have several issues: 1) The law states that ## \nabla\cdot E=\frac{1}{\epsilon 0}\rho##, but when I calculate it directly I get that ## \nabla\cdot E=0## (at least for ## r\neq0##). 2) Now ##...

Hi, I have two coupled differential equations d^2 phi(z)/dz^2=lambda*phi(z)*(phi(z)^2+psi(z)^2-sigma^2) d^2 psi(z)/dz^2=lambda*psi(z)*(phi(z)^2+psi(z)^2-sigma^2+epsilon/lambda) where lambda, epsilon and sigma are arbitrary constants. The equation subject to the bellow boundary conditions...

Can anyone help me to solve a differential equation? I want to solve ∂v(p,t)/∂t=-p^2 v(p,t)-sqrt(2/pi)∫v(p,t)[1-δ(t)R(t)]dp+sqrt(2/pi)[δ(t)R^2(t) C] with initial data v(p,0)=0 where C is constant and the integration from zero to infinty Any suggestion please? Solution by volterra integral...

I'm studying General Relativity and Differential Geometry. In my textbook, the author has written ##x^2=d(x,.)## where d(x,y) is distance between two points ##x,y\in M##. I couldn't understand what d(x,.) means. Moreover, I am not sure if this is generally true to write ##x^2=g_{\mu\nu} x^\mu...

how do you solve this equation? y´´ + k/(y^2) = 0 ? I got it from applying Newton's 2nd law of motion to an object falling from space to Earth only affected by gravitational force. Thank you!

Solve the given differential equation by separation of variables. (dy/dx)= (xy+3x-y-3)/(xy-2x+4y-8) First, I noticed when i divided both sides by the left hand side and multiplied both sides by dx, nothing canceled or seemed to work. I got to thinking. on the right hand side I preformed long...

a) On January 1 2000, the park estimated that they had 500 deer on their land. Two years later, they estimated that there were 550 deer on the land. Assume that the number of deer was changing exponentially, i.e. P(t)=ae^bt where P is the number of deer at year t, and a and b are parameters.Find...

I am looking to pick up one of these texts, but I don't really want to buy all three. Is there a considered favorite? Thanks in advance. B. O'Neill: Semi-Riemannian Geometry with Applications to Relativity T. Frankel: The Geometry of Physics B. Schutz: Geometrical Methods of Mathematical Physics

Homework Statement dy/dx = 4e-xcosxThe Attempt at a Solution [/B] I've divided dx to both sides, and now have dy = 4e-xcosx dx I've then started to use intergration by parts to the right side with u = 4e-x and dv = cosx dx Leaving y = 4e-xsinx - ∫ -4e-xsinx dx Once again I used intergration...

Homework Statement dy/dx + 2sin2pix = 0 -------Answer: y = 1/pi cos2pix + c Homework EquationsThe Attempt at a Solution I made several attempts but no success to the correct answer. The first step I made was subtracting 2sin2pix to both sides. I then used integration by parts, and this is...

I know there are a number of ways to do this problem, to increment the series etc. but, would someone please be able to explain how they get the answers for this problem simply and easily ? Thanks! A screen shot is attached

this starts as a calculus question, but springs into where i can get help with david bachman's A GEOMETRIC APPROACH TO DIFFERENTIAL FORMS second edition. looking at paul's notes cheat sheets http://tutorial.math.lamar.edu/cheat_table.aspx we have## \int \frac{1}{\sqrt{a^{2}-x^{2}}} =...

Homework Statement Identify the following differential equation as linear, separable, exact, or a combination of the three. $$1 + \frac{1+x}{y}\frac{dy}{dx} = 0$$ Homework Equations Start with ##F(x,y)=C## ##\displaystyle \frac{d}{dx}(F(x,y)) = \frac{d}{dx} (C)## ##\displaystyle...

Solve y'' - 2y' + 2y = ## e^x tanx ## What concept should we use if we know only solving first order differential equation?

I'm having some difficulty with a problem from Boyce & DiPrima's Elementary Differential Equations and Boundary Value Problems, 9th Edition. The problem comes from Section 2.8: The Existence and Uniqueness Theorem and is part of a collection of problems intended to show that the sequence...

Let V1 be the voltage across C1 and V2 be the voltage across C2. I want to solve for V1 and V2 as a function of time. My idea was to use dV1/dt=I1/C1 and dV2/dt=I2/C2. Then using circuit rules i can express I1 and I2 as functions of V1 and V2 and substitute them into the previous diff eqs...

I am having a hard time understanding the conditions that set a plane to be called a region. According to definition 2.68, a set in the plane is called a region if it satisfies the following two conditions (p. 14): 1. "Each point of the set is the center of a circle whose entire interior...

I have been working on a math problem and I keep getting the some type of PDEs. x*dU/dx+y*dU/dy = 0 x*dU/dx+y*dU/dy+z*dU/dz = 0 ... x1*dU/dx1+x2*dU/dx2+x3*dU/dx3 + ... + xn*dU/dxn= 0 dU/dxi is the partial derivative with respect to the ith variable. Does anyone know about this type of PDE...

Homework Statement Homework EquationsThe Attempt at a Solution Any help would be appreciated

I'm in my last semester of my undergraduate majoring in mathematics (focusing on mathematical physics I guess - I'm one subject short of having a physics major) and am wondering, largely from a physics perspective if it would be better to do a functional analysis course or a differential...

The usual form for tension as a result of the symmetric Cauchy stress tensor is, $$\mathbf{t} = P \mathbf{\hat{n}}$$ or better $$t_i = {P_i}^j n_j$$ Buoyancy would be $$T = \int_{\partial V}{P_i}^j n_j da$$ integrated over a closed surface. I've assumed that the stress tensor ##P##, is, in...

Hi, I'm a beginner in mechanics so I need some help with a project I started. My project consists of a small kart-like car. The car will be Rear-Wheel-Drive and Rear-Engine too (RR layout). and I am willing to use a small 110cc moped engine. I have a trike Differential Gear for the rear shaft...

Homework Statement ##y' = \frac{cos x}{sin y}## ##y' = \frac{6x^2}{y(1 + x^3)}## Homework EquationsThe Attempt at a Solution So I was working through some textbook problems and there's something about the solutions of the above equations I don't quite understand. The first one: ##\int sin...

If z = e ^ (xy ^ 2), x = tcost, and y = tsint compute dx / dt for t = pi / 2 I kind of lost in this difficult question pls help I tried putting down the xy but using ln lnz = xy^2 Product rule? Or what. This is my first time encountering this kind of question

After a big mistake in this PF, I try to post my question here, hoping it is ok. I'm looking for a more "simple" relation than Darcy's law. I try to determinate what is the relation between air speed and differential pressure in a tube where there is a restrictor. A kind of relation like V=kP...

Hi, I'm an engineer working on a subsea pipeline project. Right now I am working on a spreadsheet to calculate the differential net pressure on a sub sea pipeline. I am using API RP 1111 for offshore pipeline design. My question is the following. For any pipeline with a nonzero wall thickness...

Homework Statement (didn't know how to make piecewise function so I took screenshot) Homework EquationsThe Attempt at a Solution My issue here with this problem is that I have absolutely no idea where to start... I have read through the textbook numerous times, and searched all over the...

Textbook by Asmar. Would this class help me a lot for grad courses, like Jackson Electrodynamics or Sakurai Quantum? Debating to just finish up my upper levels and get As

During the summer, I plan on learning differential equations (ODE's and PDE's) from bottom to top, but I am unable to choose books due to a great variety present. Can you suggest books for me to read in the following order (you can add as many books in each section if you like);Ordinary...

Homework Statement ##y^{(4)} + y = 0, y(0)=0, y'(0)=0,y''(0)=-1,y'''(0)=0## My issue with this equation is not with the steps, I don't believe but the solving of the IVP, the derivatives of my solution end up being close to 32 terms long, and I was wondering if there is any shorter method I...

Homework Statement y'' - xy' + xy = 0 around x0=0 Find a solution to the 2nd order differential equation using the series solution method.Homework Equations Assume some function y(x)= ∑an(x-x0)n exists that is a solution to the above differential equation.The Attempt at a Solution How...

In some books, the differential is defined by: (a) ##df(v) = v(f) : T_pM → \mathbb {R}## while in other books, a more abstract definition is made: (b) Given two manifolds ##M,N##, ##v \in T_pM## and a map ##F :M → N## then ##dF## is defined ##dF(v)(f) = v(f\circ F) : T_pM → T_{F(p)}N##...

Homework Statement y'' + y =3*sin(2t) +t*cos(2t) Okay, so I have found the complimentary solution, and the first partial solution as listed in my work below. My problem is the work on the second partial solution. I have got all the derivatives plugged into the differential equation, my...

Hey! :o Is someone familiar with the following? We have linear differential equations with polynomial coefficients depending on x. $a_n(x)y^{(n)}+ \dots a_1(x)y^{(1)}+a_0(x)y^{(0)}=b(x)$ There are problems like if there are solutions, if the solutions are linear independent and so on and...

What is the general solution of the following hyperbolic partial differential equation: The head (h) at a specified distance (x) is a sort of a damping function in the form: Where, a, b, c and d are constants. And the derivatives are with respect to t (time) and x (distance). Thanks in advance.

Hi there, I was reading up on Holonomic constraints and came across this equation on the Wikipedia page: The page says it is a differential form. Can anyone explain the notation for me or provide a link or two to documents or pages which explain this notation? Thank you very much, Geoff

So there are these 4 differential equations problems that are ruining my day. I can't find any videos or notes for differential equations of calculus which is for some reason in my Calc 1 class. They seem kind of simple but I just can't seem to get started... any help is appreciated! 1b) When...

Homework Statement Solve the Differential Equation:[/B] When I take the partial derivative of each of these equations, I do indeed get that it is exact... However, when I do it the way my professor wants me to do it, I don't get the same result. He told us to multiply through by the common...

Homework Statement Solve the differential equation: Here is the books answer to the problem: Homework Equations This is a substitution/homogeneous first order differential equation, which can be converted into a separable differential equation. The Attempt at a Solution Where am I...

Homework Statement I believe I have solved this differential equation, yet do not know how the book arrived at it's answer... Solve the differential equation in its explicit solution form. The answer the book gives is... Homework Equations Separable Differential Equation The Attempt...

Homework Statement Solve the differential equation, explicitly. dy/dx = (2x)/(1+2y) The answer given by the book is... -1/2 + 1/2sqrt(2x - 2x^2 +4) Homework Equations Process for solving separable differential equations The Attempt at a Solution dy/dx = (2x)/(1+2y) (1 + 2y)*dy = 2x*dx...