Differential Definition and 1000 Threads

For what differential equations would having much quicker or financially cheaper methods of solving them significantly benefit scientists or engineers?

Hi all! I am trying to simulate a differential amplifier in LTSpice but I'm having some troubles. First, I would like to know if you could suggest me some "basic", scholastic, MOSFET and BJT model, like the 1N4148 for diodes. Secondly I designed this: Practically when I get the drain output...

Homework Statement [/B] Summarizing: two civilizations hate each other, one of the civilizations throws a curse at the second. The second civilization succumbs to chaos and has a change in Population each week of ΔP= -√P. That is: Pn = Pn-1-√Pn-1 Homework Equations [/B] Considering that the...

Homework Statement I have no idea how the third formula of dy/dx is derived ... Homework EquationsThe Attempt at a Solution I know that the Q = (1/n)(A)(R^2/3) [(s)(^0.5)] , Q = K [(s)(^0.5)] , so , K= (1/n)(A)(R^2/3) i know that for very wide channel , y = R A = by K= (1/n)(A)(R^2/3)...

Hello, I am currently a High School Senior who has completed Multivariable Calc (up to stokes theorem), basic Linear Algebra ( up to eigenvalues/vectors) and non-theory based ODE (up to Laplace transforms) at my local University. (All with A's) I am hell bent on taking either one of the courses...

Homework Statement Prove the formula for inertia of a ring (2D circle) about its central axis. Homework Equations I = MR^2 Where: M: total mass of the ring R: radius of the ring The Attempt at a Solution - So I need to prove the formula above. - First, I divide the ring into 4...

Homework Statement Find the order of the differential equation of y=C1sin2x+C2cos2x+C3. Homework Equations - The Attempt at a Solution [/B] I read in my book that the order of the differential equation is equal to the number of arbitrary constants but the answer given is 2. Btw I have...

Homework Statement Homework EquationsThe Attempt at a Solution I am not asking to find the answer, just wanted to know whether to use the variation of parameters or undetermined coefficients. Because this was on a test problem and I used variation of parameters instead. I know it is a...

I will use an example: -The surface is given by the intersection of the plane: y+z=2 -And the infinite cilinder: x2+y2<=1 We want to parametrize this surface, it could be done easily with: x=r cosθ y=r sin θ z=2 - r cos θ Then this surface could be written using vector notation: S= r...

Homework Statement A differential pulley carries a weight W. The chain used has N links per foot. The bigger pulley has n notches, which can hold two chain links each. The smaller pulley contains n - 1 notches, which can also hold 2 chain links. The friction is such that the ratio of the force...

Hello, does anyone have reference to(or care to write out) fully rigorous proof of Stokes theorem which does not reference Differential Forms? I'm reviewing some physics stuff and I want to relearn it. I honestly will never use the higher dimensional version but I still want to see a full proof...

Homework Statement y''-16y=2e^4x. Find general solution Homework EquationsThe Attempt at a Solution I have the homogenous equation which is c1e^-4x+c2e^4x, but I'm trying to find the particular solution for 2e^4x. I did yp=ae^4x, yp'=4ae^4x, yp''=16ae^4x, then plugged it into the equation...

Sin(3x)dx+2ycos(3x)dy=0 So far, I have ∫2ydy=-∫sin(3x)/cos^2(3x)dx. Is that right? If so, how do I integrate sin(3x)/cos^2(3x)?

I have two questions about the use of stochastic differential equation and probability density function in physics, especially in statistical mechanics. a) I wonder if stochastic differential equation and PDF is an approximation to the actual random process or is it a law like Newton's second...

Homework Statement The equation is z= e (x*y), the interesting thing is y is function of x too, y = ψ(x) Calculate the partial derivative respect to x, and the total derivative. Homework Equations Total differential: dz= ∂z/∂x dx + ∂z/∂y dy The Attempt at a Solution [/B] Well, according...

First of all I want to clarify that I posted this question on many forums and Q&A websites so the chances of getting an answer will be increased. So don't be surprised if you saw my post somewhere else. Now let's get started: When it comes to definitions, I will be very strict. Most textbooks...

Homework Statement Transform the equation: x2 * d2y/dx2 + 2 * x * dy/dx + (a2/x2)*y = 0 Using: x=1/t Homework Equations The differential of a function of several variables, and the common rules of differentiation. https://en.wikipedia.org/wiki/Derivative The Attempt at a Solution As...

Homework Statement Find the values of the constant a for which the problem y''(t)+ay(t)=y(t+π), t∈ℝ, has a solution with period 2π which is not identically zero. Also determine all such solutions Homework Equations With help of Fourier series I know that : Cn(y''(t))= -n2*Cn(y(t)) Cn(y(t+π)) =...

Hi there. I am trying to self teach how to solve partial differential equations numerically using finite differences. I know this is a complex field, that requires much more knowledge of the theory than what I actually know, but anyway I wanted to try. Anyway, I've tried to build my own...

Homework Statement For a following differential equation d^2y/dx^2-4y=(e^x)/x  Find the solution using numerical methods Homework Equations d^2y/dx^2-4y=(e^x)/x The Attempt at a Solution %num dx=0.01; x=1:dx:3; l=zeros(1,length(x)); m=zeros(1,length(x)); l(1)=1; m(1)=0.25; for...

Homework Statement A mass ##m## on a frictionless table is connected to a spring with spring constant ##k## so that the force on it is ##F_x = -kx## where ##x## is the distance of the mass from its equilibrium position. It is then pulled so that the spring is stretched by a distance ##x## from...

<OP warned about not using the homework template> Obtain a series solution of the differential equation x(x − 1)y" + [5x − 1]y' + 4y = 0Do I start by solving it normally then getting a series for the solution or assume y=power series differentiate then add up the series? I did the latter and...

solve the following differential equation with the suggested change of variables.

I have a differential equation that is essentially this: θ''(t)=c*sin[θ(t)] . I've been stymied trying to find a solution, and even when I tried using Maple, I got a nasty integral of a Jacobian amplitude. I'm tempted to use a small angle approximation, but the angle is 0≤θ≤π/2. I know this...

Specifically:

Homework Statement Write down a 3x3 matrix A such that the equation ##\vec{y}'(t) = A \vec{y}(t)## has a basis of solutions ##y_1=(e^{-t},0,0),~~y_2 = (0,e^{2t},e^{2t}),~~y_3 = (0,1,-1)## Homework EquationsThe Attempt at a Solution I was thinking that, it looks like the matrix would have to...

Homework Statement I am trying to solve the following: y'''-9y'=54x-9-20e^2x with y(0)=8, y'(0)=5, y''(0)=38 Homework EquationsThe Attempt at a Solution The right answer is: y= 2+2e^3x+2e^(-3x)-3x^2+x+2e^2x I am only wrong on the coefficients C2 and C3. Where did I mess up in my solution?

Homework Statement Consider the following differential equation $$\frac{\partial^{2}\phi}{\partial t^{2}}-\nabla^{2}\phi = \phi(a-b\phi^{2}), \qquad a>0.$$ I would like to prove that $\phi=0$ is an unstable solution of this equation. Homework Equations The Attempt at a Solution Do you...

Homework Statement I am given (y^2 + y sin x cos y) dx + (xy + y cos x sin y) dy = 0, y(0) = π/2 . I need to solve this Homework EquationsThe Attempt at a Solution At this point they still aren't exact, so I gave up. I can't figure out what the problem is. Is it possible that I have to...

Hello everyone. So I wanted to get some opinions on what some of you thought was a better choice, as far taking PDE's or classical mechanics 2 goes. First let me start off by giving a little info; I've already taken calc 1-3 and ordinary differential equations, physics 1 & 2...

Hello to everybody, Since 3 days, I've been trying to obtain Eq. (173) from https://ned.ipac.caltech.edu/level5/Sept03/Trodden/Trodden5.html I know I need to derivate with respect to a, but it is being impossible to obtain the final answer. Can anybody help me with a detailed derivation...

Hello everybody, If I define z_\mu = \frac{\partial{\phi}}{\partial{x^{\mu}}}, \, \mu = 0,1,...,n , (for some scalar function phi of x=(x_0,...,x_n)) how is then \frac{\partial{}}{\partial{z_{\mu}}} defined or rather what is it equal to? How would you call this expression? the inverse of a...

Hi folks, When you have a differential equation and the unknown function is complex, like in the Schrodinger equation, What methods should you use to solve it? I mean, there is a theory of complex functions, Laurent series, Cauchy integrals and so on, I guess if it would be possible to...

Homework Statement How exactly they combined equation1 and equation2 and got that system? I don't get that part. Homework Equations A*(dy/dt)= -k*y eq1 A*(dz/dt)=ky-kz eq2 The Attempt at a Solution I tried substituting the 1st ky in the 2nd equation and then differentiating but I don't...

Hi I am working on an assignment which is has asked us to derive an expression for a differential number count of supernovae in a euclidean flat non-expanding space. I am bit perplexed by this question and am wondering whether it is a trick question. We are allowed to do research to find an...

In the following equation: $$g'(x) = f'\left( x + \frac{c f'(x)}{\sqrt{ 1 + f'(x)^2 }} \right)$$ find $g(x)$ with respect to $f(x)$ where $c$ is any constant.

Hi, another question I am having trouble with so my thought at the moment is to integrate a(t), which results in 1/2at^2 which is the kinematic equation for distance and then solve for the equation to equal 100. Just doesn't seem right to me and possibly too easy a solution.. think I am...

Hi, need some help on the following question. Just want to check on part a on the followingv=4/3\pi.r^3 dv = 4\pi.r^2 dr dv/dt = 4\pi.r^2 dr/dt dr/dt = (dv/dt)/ 4\pi.r^2 dr/dt = (-KA)/4\pi.r^2 dr/dt= -K part B need some help Thanks Tom

I'm currently studying the sensitivity of polynomial roots as a function of coefficient errors. Essentially, small coefficient errors of high order polynomials can lead to dramatic errors in root locations. Referring to the Wilkinson polynomial wikipedia page right...

(1) ##\frac{d^{2}y}{dx^{2}}=0## (2) ##\frac{d^{2}y}{dx^{2}}=k^{2}y##, where k is a real positive number.

Homework Statement Find the full response. Assume Vin is a squarewave with Vpp =10V and Vamp = +5V Homework Equations KCL The Attempt at a Solution My teacher gave this solution but I don't really understand some parts of it. Full response = Natural response + forced response Thevenin...

I am given a modified SIR model in which the rate of decrease of susceptibles S is proportional to the number of susceptibles and the square-root of the number if infectives, I. If the number R of those who have been removed or recovered increases in proportion to the infectives, we have the...

Homework Statement Liquid is pouring into a container at a constant rate of 30cm^3s^-1 At time t seconds liquid is leaking from the container at a rate of 2/15 V cm^3s^-1, where V cm^3 is the volume of liquid in the container at that time. Show that -15 dV/dt = 2V - 450Homework Equations ...

ρCp (∂T/∂t) + k (∂2T/∂x2) = exp(-σt2)exp(-λx2)φo i have this equation... i was thinking of taylor series expansion to solve it and make it easier... any ideas on how to solve?

Homework Statement Homework EquationsThe Attempt at a Solution Nodal Equations By property of OpAmp, V2=Vo eq1:\frac{V_{1}-V_{in}}{R_1}+\frac{V_{1}-V_{o}}{R_2}+C_2*(\dot{V_1}-\dot{Vo}) eq2: V_1=C_1R_2\dot{V_o}+V_o eq3: \dot{V_1}=C_1R_2\ddot{V_o}+\dot{V_o} Sub 2 & 3 into 1...

Homework Statement Homework Equations The Attempt at a Solution Because we are only looking at a cross section, I tried to reduce 5.3 down to just being a function of R and Theta. However I reasoned that there should be, based on this problem, no dependence on Theta either, so I figured I...

Homework Statement Identify the type of singularity at x=0 for these differential equations x*Sin[1/x]*y''[x]+y[x]==0 x^2*y''[x]+Sin[1/x]*y[x]==0 Homework Equations A Singular point is regular if f(x)(x-x_0)^n is defined as x approaches x_0 and is analytic in a near a neighborhood of that...

Are there differential equations that, for some reason, don't have a Green function? Are there conditions for a DE to satisfy so that it can have a Green function? Thanks

Some time ago I was looking around the web for the use of differential equations in General Relativity. Then I found a definition (below) of differential forms, but I noted that the definition on my book is different from this one. Could someone tell me if it is right?

A one-dimensional dynamical system is given by $x′ = f(x), t \in [0,+\infty)$, where $f : \mathbb{R} \to \mathbb{R}$ is the smooth function defined as follows: $$f(x) = \begin{cases} x^4 \sin \left(\frac{1}{x}\right) & x \neq 0\\ 0 & x = 0. \end{cases}.$$ Find all the equilibrium points and...