Differential Definition and 1000 Threads

Homework Statement [/B]Homework Equations The Attempt at a Solution I've highlighted two equations on the screenshot. How did it proceed from the first to the second? I'm actually confused with the absolute values. What is the idea behind getting rid of the first absolute value(1-5v^2) while...

Homework Statement dx/dt = (1+x2)et ; x(0) = 1 1/1+x2 dx/dt = et ∫ 1/1+x2 (dx/dt) * dt = ∫ et dt ∫ 1/(1+x2) dx = ∫ et dt arctan(x) = et + c so x(t) = tan (et+c) Homework EquationsThe Attempt at a Solution dx/dt = (1+x2)et ; x(0) = 1 1/1+x2 dx/dt = et ∫ 1/1+x2 (dx/dt) * dt = ∫ et dt ∫...

To motivate the question, Andy Strominger recently put out a paper on calculating the Sagnac shift of counterrotating beams due to the angular momentum flux of a passing gravitational wave. See here: http://arxiv.org/abs/1502.06120. But consider now two nearby freely falling gyroscopes...

Hello I have a system of differntial equations: dx/ds = sin(p) dy/ds=cos(p) dp/ds = k dk/ds = -1/EI(s)*(k*dEI/ds+f*sin(p)) x(0)=y(0)=p(0)=p(L)-pl = 0 These are nonlinear differential equations. I should use some sort of nonlinear finite difference. But I do struggle to setting up the finite...

Got a bit of a long and nutty question here. So I got a nutty question from my Calc 1 class and was wondering if anyone could help me out A section of road, represented by the line y = x + 4 when x ≤0, is to be smoothly connected to another section of road, represented by y = 4 –x when x ≥4...

I will try to explain this with an analogy. Let's have this equation: x^2 =9 And let's assume I don't know algebraic methods to solve it, so I create a list using excel with different values. And I see that if I put x=4 it doesn't work, if I put x=5 it is even worse and so on. But If I put...

Homework Statement http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-003-signals-and-systems-fall-2011/assignments/MIT6_003F11_sol01.pdf http://i.imgur.com/8qj5cWE.png #6 Part B Homework Equations None[/B]The Attempt at a Solution Don't understand why we care about...

Hello, I am a math major and I was wondering if you guys knew what would be a good rigorous differential equations text. I really like rigor (like Rudin analysis style rigor or whatnot), instead of the typical books that just focus on the method. I want the proofs and everything. I also would...

Hello! (Wave) If we have the initial value problem $$h''(t)=-\frac{R^2 g}{(h(t)+R)^2} \\ h(0)=0, h'(0)=V$$ we have the fundamental units: $T,L$ such that $T=[t], L=[h], L=[R], LT^{-1}=[V], LT^{-2}=[g]$ and we get the independent dimensionless quantities $\pi_1=\frac{h}{R}...

Hey all! I have been trying this problem for a while and can't seem to get the same answer as the solution. If someone can tell me where I am going wrong, that would be much appreciated. I am very close to the solution, but I am missing a term in the denominator. Everything is shown below! Thank...

Hello, I wanted to study the behaviour of electrons in a spatially bounded system. I want to have a larger number of electrons, but I took 3 to start with and arrived at this system of coupled equations: \begin{align}\begin{bmatrix} \mathbf{\ddot{x_{1}}}\\ \\ \mathbf{\ddot{x_{2}}}\\ \\...

I've been struggling since starting to study differential geometry to justify the definition of a one-form as a differential of a function and how this is equal to a tangent vector acting on this function, i.e. given f:M\rightarrow\mathbb{R} we can define the differential map...

Homework Statement I am trying to show that ##a(x)[u(x),D^{3}]=-au_{xxx}-3au_{xx}D-3au_{x}D^{2}##, where ##D=d/dx##, ##D^{2}=d^{2}/dx^{2} ## etc.Homework Equations [/B] I have the known results : ##[D,u]=u_{x}## ##[D^{2},u]=u_{xx}+2u_{x}D## The property: ##[A,BC]=[A,B]C+B[A,C] ##*The...

Homework Statement Find the differential of axb Homework EquationsThe Attempt at a Solution Really not sure where to start, honestly. Thanks in advance :)

It has been a while since I was involved with my differential equations. I am a mech student. I was trying out a sample problem from the dynamics book and came upon this equation. k = some constant of proportionality for a spring pushing back a spring mounted slider. (1/k) arcsin(ks/v_0) = t...

Hello! (Wave) I want to find the solution $\psi$ of the non-linear differential equation $y'=1+y^2$ that satisfies the condition $\psi(0)=0$. (Notice that the solution $\psi$ exists only for $- \frac{\pi}{2}< x < \frac{\pi}{2}$) We notice that: $(tan^{-1})'(x)=\frac{1}{1+x^2} (\star) \left(...

Not a homework question, I'm just curious, I know this has been asked a few times, but what exactly is happening when you move dx over to the other side of dy/dx=f'(x), is it like the point slope form ∆y=m∆x, or is it applying the differential to both sides, I've always been told a rigorous...

Hi all, first post here. I'm a junior Physics/Math double major at UMass Amherst, playing with some problems over the summer. I'll get right into it. A rope with constant tension T is deflected through the angle 2\theta_{0} by a smooth, fixed pulley. What is the force on the pulley? It is...

Homework Statement dv/dt = 9.8 - 0.196v Set in correct form: dv/dt + 0.196v = 9.8 Since p(t) = 0.196, u(t) the integration factor is given by: u(t) = e∫0.196 dt Multiply each term by u(t) and rearrange: (e∫0.196 dt)(dv/dt) + (0.196)(e∫0.196 dt)(v) = (9.8)(e∫0.196 dt) From now on we will set...

Homework Statement dX = U/V dV + U/p dp Write the differential of X in terms of the independent variables.Prove that this is an exact differential.Use the ideal gas equation of state to verify that X is actually the internal energy and that it satisfies the above equation. Would...

Homework Statement you are given a family of curves, in this case i was given a bunch of circles x^2+y^2=cx, sketch these curves for c=0,2,4,6, both positive and negative, solve the equation for c and differentiate both sides with respect to x and solve for dy/dx. You obtain an ODE in the form...

hello all.glad to be here! please in the attached document, column 5 and 6 which represents the differential and cumulative frequency distributions were obtained using equations (5) and (6). I'll be mighty grateful if anyone can give me a step by step breakdown of how it was done?? Many thanks...

A question from a classical mechanics past paper described a particle of mass ##m## that had a pair of horizontal identical springs of spring constant ##k## attached on either side and that the mass is free to move horizontally. The mass is also placed on a table that gives rise to an...

To be honest, I don't know any physics. I am a high school student who has taken high school physics, but America's education system isn't known for teaching much more than Newton's laws. I have, however, taken Multivariable/Vector calculus, so I have a decent math background. I was wondering...

It is a general doubt about the following equation: Imagine I want to calculate an unknown function y(x), and my starting equation is of the type y(x)^{2}=\frac{1}{x^{2}Log^{2}(A(x)y(x)^{2})} , then, am I allowed to start with the equation y(x)=\frac{1}{xLog(A(x)y(x)^{2})} and...

Homework Statement Solve the system using differential operators. Determine the # of arbitrary constants and then compare to your solution. Homework Equations D substitution: replace x' with Dx and y' with Dy The Attempt at a Solution I have the solution to this one, but I'm working...

Homework Statement 1. y" + y = tanx, solve this DE. 2. dP/dt = P(1 - P) where P = (c1et / 1 + c1et), verify that P is a solution to this DE. 3. Given the pair of functionsx and y, show they solve this system: dx/dt = x + 3y dy/dt = 5x+3y x = e-2t + 3e6t y = -e-2t + 5e6tThe Attempt at a...

Homework Statement I have two equations. cos(θ)wφ + sin(θ)wφ = 0 (1) And ## \frac{w_φ}{r}## + ∂wφ/∂r = 0 (2) Find wφ, which is a function of both r and theta. Homework EquationsThe Attempt at a Solution I end up with two equations, having integrated. wφ=## \frac{A}{sinθ}## from (1)...

Homework Statement A long cylindrical wire of radius R0 lies in the z-axis and carries a current density given by: ##j(r)= j_0 \left( \frac{r}{R_0} \right)^2 \ \hat{z} \ for \ r< R_0## ##j(r) = 0 \ elsewhere## Use the differential form of Ampere's law to calculate the magnetic field B inside...

Homework Statement The website says this: "It is Linear when the variable (and its derivatives) has no exponent or other function put on it. So no y2, y3, √y, sin(y), ln(y) etc, just plain y (or whatever the variable is). More formally a Linear Differential Equation is in the form: dy/dx +...

Homework Statement data[/B] Solving differential k forms. Homework Equations I don't want to give any exact problems from my problem set. The Attempt at a Solution solution.[/B] The text I'm using, CH Edwards, is very abstract in this section and the explanation over a sped up, last class...

I don't understand this first order differential equation: https://lh5.googleusercontent.com/UUpQF4YjmjJRPvFuzGg2MhpMMMDyi2KFZPCKMKVIXGREc1owvXDzGR0bcA=s600 How is it possible to get an exponent as answer?

Homework Statement A particle moves in a straight line with velocity given by ## dx/dt = x +1 ## ( x being distance described). The time taken by the particle to describe 99 meters is? Homework Equations NA The Attempt at a Solution Getting ## ln(x+1) = t + C## How to determine the constant...

1. (16+x2)-xy'+32y=0 Seek a power series solution for the given differential equation about the given point x0 find the recurrence relation. So I used y=∑Anxn , found y' and y'' then I substituted it into the original equation, distributed, made all x to the n power equal to xn, made the...

My school requires me to take a calc 3 course and differential equations for my major. I am scheduled right now to take differential equations in the summer, and calc 3 in the fall of this year. My school recommends they be concurrent classes, but I'm just too strapped down by my already almost...

Homework Statement find the inverse laplace transform. 1/(s^3 + 7s) Homework Equations sin(kt) = k/(s^2 + k^2) cos(kt) = s/(s^2 + k^2) The Attempt at a Solution so this one is different from all the others I have done because it involves an imaginary number and I am not sure what the rule...

1. I am supposed to find dx and dy. I think I am missing a step or a general idea. I spent quite some time figuring out what rules should I use and the only sequence I can think of is quotient rule and chain on the (x2 +y2)1/2 term. The answer that I find is ((xy(3x2+2y2))/(x2+y2)3/2 . On the...

The equation looks like: ##x''(t)+b x'(t)+cx(t)+ d x^3(t)=0##. This is the motion of a particle in a potential ##cx^2/2+d x^4/4## with friction force ## b x'##. In my case, the friction term is very small and the particle will oscillate billions of times before the magnitude decreases...

Homework Statement Solve d2θ/dη2 + 2η(dθ/dη) = 0, to obtain θ as a function of η, where θ=(T-T0)/(Ts-T0) EDIT: I should add that this is a multi-part problem, and η is given as η=Cxtm. We had to use that to derive the equation in question above.. So I don't know if this is supposed to be...

Homework Statement y3(dy/dx) = (y4 + 1)cosx 2. The attempt at a solution I solved for the homogeneous equation which is y = Ce-sinx Where C is some constant for the particular solution I tried Asinx + Bcosx where A and B are constants but when subbing in it's gets very messy. How should...

Homework Statement Calculate gain (u_o/u_i) for a differential amplifier with symmetric output. Both transistors have the same transconductance gm. Transistor output resistance r_0 is neglected here. circuit: http://sv.tinypic.com/view.php?pic=14cea8p&s=8#.VSf7Evl_vxM Homework Equations...

Homework Statement Consider a system composed of two species X and Y with fractional populations x and y, respectively, where x+y=1. The two species interact in such a way that the differential equation for x is: \begin{equation} \frac{dx}{dt}=xyA_{0}e^{-\alpha t} \end{equation} where $A_{0}$...

Homework Statement The following series of differential equations represents a projectile's path when solved (g=9.81): Modify this series of differential equations to account for an additional force F with vector components a and b acting on the projectile. Here is a sample plot of this...

Homework Statement Verify that the functions y1(x) = x and y2(x) = 1/x are solutions of the differential equation y'' + (1/x)y' - (1/x2)y = 0 on I = (0,∞). Show that y1(x), y2(x) is a basis of the solution space of the differential equation. The Attempt at a Solution For the first part I'll...

Homework Statement The differential equation is xy'-2y= x3ex Check the solution y=x2 ex Homework Equations Just plug in The Attempt at a Solution y' = x2ex + 2xex Having problem solving for x.

I am currently looking at grad schools, and I am wondering if anyone knew who are the leading researchers in differential geometry. I know that question is a little vague considering how diverse differential geometry is, but I was hoping that something could direct me in the right direction...

In one of my classes, I should give a talk about pair production cross section in front of the class and so I'm now searching for resources. But I can't find a place where the differential cross section for pair production process is given. Anyone knows somewhere I can find it and , preferably...

I am trying to understand Differential Topology using several textbooks including Lee's book on Smooth Manifolds. I am looking for some good online lecture notes at undergraduate level (especially if they have good diagrams and examples) in order to supplement the texts ... Can anyone help in...

Homework Statement 2. Homework Equations [/B] Small Signal Equivalent Circuit, Kirchhoff Current Law, and BJT equations mentioned in the question. The Attempt at a Solution It looks like I did something wrong. Can someone help me with fixing this?

Hi all, I found online that most professional websites suggest using differential probes to calculate power, along with a current probe, for a DUT. What advantage does the diff probe give us for power calculation? Thanks