Differential Definition and 1000 Threads

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...

Homework Statement I am trying to solve this \begin{align} d X_t = - b^2 X_t (1 - X_t)^2 dt + b \sqrt{1 - X_t^2} dW_t \end{align} where $b$ is a constant. Note that I have the answer here and can provide it if necessary. But I want to know how one would come up with it. Homework EquationsThe...

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

What is the general method for solving a differential equation of the form \begin{equation} \frac{\partial^{2}z}{\partial x^{2}}+\frac{\partial^{2}z}{\partial y\partial x}=C\end{equation} where C is a constant.

Homework Statement Solve for y using the substitution: z = 1/(y^5) dy/dx + y/x = (y^6)(x^3) Homework Equations (dz/dx) = (dz/dy) x (dy/dx) The Attempt at a Solution I formed an equation for dz/dx but cannot separate the variables in order to integrate. Can someone tell me where I've gone...

If we have,$$A=d[(\bar{\alpha}-\alpha)(dt+\lambda)]$$ where $$\alpha$$ is a complex function and $$\lambda$$ is a 1-form. t here represents the time coordinate. If we want to calculate $$d\star A=0$$ where $$\star$$ is hodge star, we get if I did my calculations correctly...

An electric vehicle of mass ##m## moves along the ##0-x## axis according to the law: m\frac{\mathrm{d} v(t)}{\mathrm{d} t} = T(t)-\mu mg-kv(t)^{2} (ma = Thrust - Friction - Drag) It is known that: P(t) = T(t)v(t) (Power = Thrust * Speed) Find the thrust ##T(t)## in such a way that the...

Homework Statement Need to prove that: (v⋅∇)v=(1/2)∇(v⋅v)+(∇×v)×v Homework Equations Vector triple product (a×b)×c=-(c⋅b)a+(c⋅a)b The Attempt at a Solution I know I could prove that simply by applying definitions directly to both sides. I haven't done that because that is tedious, and I...

Homework Statement Find the distance which an object moves in time t if it starts from rest and has an acceleration d^2x/dt^2 = ge^-kt. Show that for small t the result is approx "x=(gt^2)/2" and show that for very large t, the speed is approximately constant. the constant is called the...

Hey! :o I want to find the solution of the following initial value problem: $$u_{tt}(x, t)-u_{xt}(x, t)=f(x, t), x \in \mathbb{R}, t>0 \\ u(x, 0)=0, x \in \mathbb{R} \\ u_t(x, 0)=0, x \in \mathbb{R}$$ using Green's theorem but I got stuck... I found the following example in my notes...

Hello! (Wave) The following differential equation is given: $$(1-x^2)y''-xy'+p^2y=0, p \in \mathbb{R}$$ Find the general solution of the differential equation at the interval $(-1,1)$ (with the method of power series). Are there solutions of the differential equation that are polynomials...

Homework Statement Hello, I was just looking for a quick tip: If I have three distinct solutions to a second order linear homogeneous d.e, how would I show that the wronskian of (y1,y2,y3)(x)=0? I know how to show the wronskian is not zero for a linearly independent set, but I'm confused...

Apologies if this isn't quite the right forum to post this in, but I was unsure between this and the calculus forum. Something that has always bothered me since first learning calculus is how to interpret dx, essentially, what does it "mean"? I understand that it doesn't make sense to consider...

Homework Statement This problem has been stumping me for days now, I'm sure I'm missing something simple as it's only worth a small number of marks on the coursework. Any help would be appreciated. I've been asked to re-express the equation of hydrostatic equilibrium: dP/dr = - Gm/4πr4...

Homework Statement hello all, Suppose y is a solution of the d.e: y"+p(x)y'+q(x)y= q(x) on the interval (-1,1) with y(0)=1 and y'(0)= 1. What is y? Homework Equations I used the auxiliary equation: m^2+p(x)m+q(x)= q(x) The Attempt at a Solution My question is can I do this? I can cancel...

Hello everyone, So I am working on a differential drive vehicle... max weight 6kg and using two stepper motors centred on a circular shaped flat body. I want to try and work out if these stepper motors have enough torque to drive the thing. I am a second year engineering student, but I haven't...

A friend recently gave me a book on quantum mechanics. It's called Introduction to quantum mechanics. It's by David j griffiths. I am currently taking multivariable calc.I am taking linear algebra next semester. I want study this book, but I am wondering what mathi I need. My friend told me I...

Homework Statement Show that the radial eigenfunction unr,l is a solution of the differential equation: ħ2/2me×d2unr,l/dr2+[l(l+1)ħ2/2mer2 - e2/4πε0r]unr,l=Enr,lunr,lHomework Equations The radial function is R(r)=u(r)/r, so that the expression on the RHS is E×u. The Attempt at a Solution I know...

Homework Statement The Attempt at a Solution The first part is fairly simple I think. It's just rate of accumulation = rate of generation - rate of output(losses) I'm not too sure how to solve this differential equation. I divide the whole equation through by mc and rearrange but I keep...

When solving a separable differential equation, my textbook says this: ln|v-49|=-t/5+C→ |v-49|=e-t/5+C→ v=49+ce-t/5 What happened to the absolute values? I think it has something to do with the exponential always being positive.

Homework Statement dy/dx=2xcos(y)-xy^3[/B]Homework EquationsThe Attempt at a Solution dy/dx=2xcos(y)-xy^3=x(2cosy-y^3) dy/(2cosy-y^3)=xdx [/B] I can not integrate the left side of the equation. Can someone help me please?

Homework Statement x(d^2y/dx^2)+dx/dt+xy=0 Homework EquationsThe Attempt at a Solution At first I thought it was an ODE, but then I found out the derivative was respect to to variables x and t. I am not sure if it is an ODE or PDE. What are the dependent and independent variables in the...

Homework Statement Find the value of the 2-form dxdy+3dxdz on the oriented triangle with (0,0,0) (1,2,3) (1,4,0) in that order. Homework EquationsThe Attempt at a Solution I have tried various subtraction of these coordinates and applying them to the formula but the answer is in the back of...

I'm designing a differential mount and am trying to wrap my head around the pitch loads the mount sees. My question is with a 1000 Ft/lb input torque will the ring and pinion ratio effect the torque that the mount must resolve? The differential is a sub-frame mounted IRS assembly, Nissan R230...

I came across a few problems in the Kleppner and Kolenkow book in which you must find the force of tension at specific lengths on a rope of mass m. They said you must use differential equations to solve these types of problems. How can you solve and use differential equations like this to get...

I am trying to calculate differential cross-section for partonic collisions (QCD) like q + q \rightarrow q +q q + \bar{q}\rightarrow q + q g + g \rightarrow g + g I can't find those calculations done anywhere, just the results and maybe some middle tips, that's all. As you may know those...

Homework Statement Good day all! I'm stumped on a question: If I fire a bullet straight up what will be the initial velocity such that the bullet doesn't come back down? I need to model a differential equation (it will be first order) some how! Also, Gravity is not constant, but rather, the...

Hello! (Smile) I am looking at the following exercise: Let $I=(0,1)$. Find the solution $\phi$ that has a continuous derivative in $\mathbb{R}$ and satisfies : $$y''=0 \text{ in } I \\y''+k^2y=0 \text{ apart from } I, \text{ where } k>0$$ and furthermore $\phi$ has the form...

Hi everyone, First of all, this is an awesome place :) I'm looking for a differential equation book, with partial differential equation (and Fourier series solution) that really goes into physics. I'm a 3-year undergrad student in Physics so I already know a little about it. By the way, for now...

I'm going through the solution to a problem that was assigned to my class and there's a step I don't really understand which I think is a concept I'm misunderstanding. 1. Homework Statement The curved surface of a cylinder of radius R and length L is insulated. The face at x = L is maintained...

Good afternoon, I've been working my way through Serge Lang's series of textbooks, and I recently completed A First Course in Calculus. I'm currently working through the sequel to that book, Multivariable Calculus, and that should keep me tied up for at least two months. Looking ahead...

Homework Statement Is the equation (x2sinx + 4y) dx + x dy=0 linear This problem also asks me to solve it, but I don't have a problem with that part. Homework Equations An equation is linear if the function or its derivative are only raised to the first power and not multiplied by each other...