Differential Definition and 1000 Threads

Hi, last semester I "solved" a full differential equation and the answer was (see the picture). What does it mean? Can I make a graphic with it or what? I really don't get it. *Arrows are just a continuation of the main formula*

I am currently looking at section IIA of the following paper: https://arxiv.org/pdf/gr-qc/0511111.pdf. Eq. (2.5) proposes an ansatz to solve the spheroidal wave equation (2.1). This equation is $$ \dfrac{d}{dx} \left((1-x^2) \dfrac{d}{dx}S_{lm} \right) + \left(c^2x^2 + A_{lm} -...

I ordered Differential Equations and Boundary Value Problem ( Computing and Modelling) by Edwards and Penney. There are several things in the book which I don't like Too much focus is given to modelling, almost every topic is explained not from mathematical point of view but from application...

[Mentor Note -- This thread start is by a new member from the recent MHB forum merger] Hello Guys, I want to find a friend with whom I can discuss differential equations! I would like to do that via WhatsApp or zoom applications. I am interested in applications of differential equations ( for...

I am currently reading about small signal analysis of a MOSFET differential amplifier. The text I am using has the below two figures for a common-mode equivalent circuit for the amplifier. The first makes sense to me except where it calls it a "Norton equivalent circuit", whereas I thought a...

Is there a good rubric on how to choose the order of polynomial basis in an Finite element method, let's say generic FEM, and the order of the differential equation? For example, I have the following equation to be solved ## \frac{\partial }{\partial x} \left ( \epsilon \frac{\partial u_{x}...

Hello, there. I am trying to solve the differential equation, ##[A(t)+B(t) \partial_t]\left | \psi \right >=0 ##. However, ##A(t)## and ##B(t)## can not be simultaneous diagonalized. I do not know is there any method that can apprixmately solve the equation. I suppose I could write the...

Hi, The following circuit is given, where the switch S is closed at time t=0. a) Set up the general differential equation (DE) for the current i(t) and bring the result into the following form## \frac{di(t)}{dt} +c_1 i(t)=c_0,## with the constant terms c0 and c1. Hint: Determine the DE using...

Hello everyone. I hope anyone can help me with this problem. I will greatly appreciate it. Willing to compensate anybody to answer this problem correctly for me.

My approach for part (a), ##\dfrac{dp}{dt}+P(t)=100## I.f=## e^{\int 1 dt} = e^t## Therefore, ##(e^t p)^{'}=100e^t## ##e^tp=\int 100e^t dt## ##e^tp=100e^t+k## Applying initial condition, ##p(0)=2000## ##2000=100+k## ##k=1900## Therefore, ##e^tp=100e^t+1900## ##p=100+1900e^{-t}##...

Hi ... I have written the equation of family of straight lines which are tangent to the circle as : y=(-m/n)x+(m^2/n)+n line intersects circle at : (m,n) But I can't understand how to find differential equation of this ... I will be appreciated if anyone has extra time to give me a little...

Hello! Disclaimer: I am not really sure in which forum I should post this problem since the homework is electrical engineering,but the problem I am facing is of mathematical nature (at least I think). Consider this circuit; The given RC network contains the resistors R1 = 200 Ω and R2 = 300...

Can someone help me understand the answer to this differential? I have the following expression where Now what I can understand the differential of what will be the following?

If the right-hand side is zero, then it will be a wave equation, which can be easily solved. The right-hand side term looks like a forced-oscillation term. However, I only know how to solve a forced oscillation system in one dimension. I do not know how to tackle it in two dimensions. I have...

My question i am trying to solve: I have successfully done first order equations before but this one has got me a little stuck. My attempt at the general solution below: $${5} \frac{\text{d}\theta}{\text{d}t}=-6\theta$$ $${5} \frac{\text{d}\theta}{\text{d}t} =\frac{\text{-6}\theta}{5}$$...

The solution in my book: 5/4 = 1.25. That is 25 % more. What I came up with: I thought that now we have totally 9 players. So A: 4/9 and B: 5/9. The difference is 1/9 which is about 11%! A friend told me : The difference between B & A is 5-4=1 The changing rate is (5-4)/5 = 0.2 ! So B has 20...

I am going through this page again...just out of curiosity, how did they arrive at the given transforms?, ...i think i get it...very confusing... in general, ##U_{xx} = ξ_{xx} =ξ_{x}ξ_{x}= ξ^2_{x}## . Also we may have ##U_{xy} =ξ_{xy} =ξ_{x}ξ_{y}.## the other transforms follow in a similar manner.

Hello, I know that this question might be a bit silly but I am confused about plotting a normalized differential cross section. Suppose that I have a histogram with the x-axis representing some observable X and the y-axis the number of events per bin. I want the y-axis to show the normalized...

*** MENTOR NOTE: This thread was moved from another forum to this forum hence no homework template. Summary:: Trying to find transfer functions to design a block diagram on simulink with a PID controller and transfer functions for a water tank system. ----EDIT--- The variables and parameters...

Summary:: Differential equation of motion, parabola Hi. I've tried resolve this problem but I have two doubts. The first is about the differential equation of motion because I can't simplify it to the form y" + a*y' + b*y = F(t). I'm not sure if what I got is right. My second doubt is that I...

I'd like a good set of notes or a textbook recommendation on how to approach vector differential equations. I'm looking for something that isn't specific to one type of application like E&M, fluid dynamics, etc., but draws heavily from those and other fields for examples. I'd strongly prefer a...

I am doing a University lab project where I measure positions of sunspots (using images from NASA's SDO) and use them to calculate the rotation of the Sun. Currently, all is going well: I have the angular velocity of several sunspots at varying heights. However, I want to be able to find the...

Hi, PF Here is the text I've taken a look at file:///C:/Users/usuario/Desktop/2001_JMT_Girep.pdf And the article I'm looking for: Artigue M. and Viennot L. Some aspects of students' conceptions and difficulties about differentials, Misconceptions and Edu. Strategies in Sci&Math. Cornell...

Any suggestions? Online courses or videos?

Hello! Consider this partial differential equation $$ zu_{xx}+x^2u_{yy}+zu_{zz}+2(y-z)u_{xz}+y^3u_x-sin(xyz)u=0 $$ Now I've got the solution and I have a few questions regarding how we get there. Now we've always done it like this.We built the matrix and then find the eigenvalues. And here is...

Hello. Considering this DE; $$ x^7 x' = (x^8-300)t^6 $$ with inital value x(0) = -2 Now the solution for the initial value should be C = -44; And for x(t) I get ; $$x(t) = (-44 e^{\frac{8}{7} t^7} + 300)^{\frac{1}{8}}$$ Now to get the biggest domain of definition I did this; $$ -44...

I have a few questions about the negative Bendixon criterion. In order to present my doubts, I organize this post as follows. First, I present the theorem and its interpretation. Second, I present a worked example and my doubts. The Bendixson criterion is a theorem that permits one to establish...

Why are n-forms called differential forms? What is differential about them? And why was the dx notation adopted for them? It must have something to do with the differential dx in calculus. But dx in calculus is an infinitesimal quantity. I don't see what n-forms have to do with infinitesimal...

I have the following differential equation, which is the general Sturm-Liouville problem, $$ \dfrac{d}{dx} \left[ p(x) \dfrac{d\varphi}{dx} \right] + \left[ \lambda w(x) - q(x) \right] \varphi(x) = 0\ , $$ and I want to perform the change of variable $$ x \rightarrow y = \int_a^x \sqrt{\lambda...

From my working...I am getting, ##xy=####\int x^{-1/2}\ dx## ##y##=##\dfrac {2}{x}##+##\dfrac {k}{x}## ##y##=##\dfrac {2}{x}##+##\dfrac {6}{x}## ##y##=##\dfrac {8}{x}## i hope am getting it right...

Starting from equation \frac{dy}{dx}=\int^x_0 \varphi(t)dt we can write dy=dx\int^x_0 \varphi(t)dt Now I can integrate it \int^{y(x)}_{y(0)}dt=\int^x_0dx'\int^x_0\varphi(t)dt Is this correct? Or I should write it as \int^{y(x)}_{y(0)}dt=\int^x_0dx'\int^{x'}_0\varphi(t)dt Best wishes in new year...

Hello everyone, I wanted some help deciding which elective to choose. I am a junior and for my next semester I have the option to pick either Differential Geometry-I or Quantum Information. I am confused which one to choose. We will be doing QMII as a compulsory course next semester and I have...

This is the question; This is the solution; Find my approach here, ##x####\frac {dy}{dx}##=##1-y^2## →##\frac {dx}{x}##=##\frac {dy}{1-y^2}## I let ##u=1-y^2## → ##du=-2ydy##, therefore; ##\int ####\frac {dx}{x}##=##\int ####\frac {du}{-2yu}##, we know that ##y##=##\sqrt {1-u}## ##\int...

How is the order of a partial differential equation defined? This is said to be first order: ##\frac{d}{d t}\left(\frac{\partial L}{\partial s_{i}}\right)-\frac{\partial L}{\partial q_{i}}=0## And this second order :##\frac{d}{d t}\left(\frac{\partial L}{\partial...

hi, i am going through differential equations which are nonlinear and singular - like Lane-Emden equation etc. my question is how to tackle singularity - while coding. regards

It seems to me there is a little of confusion about the definition of gradient. Take for instance a smooth function ##f## defined on a differentiable manifold. Which is actually its gradient at a given point ? Someone says gradient is the vector ##\nabla f## defined at each point, whilst...

I am reading on this part; and i realize that i get confused with the 'lettering' used... i will use my own approach because in that way i am able to work on the pde's at ease and most importantly i understand the concept on separation of variables and therefore would not want to keep on second...

What the hell is this and is it solvable?

Hi, I would like to ask for a clarification about the difference between a differential k-form and a generic (0,k) tensor field. Take for instance a (non simple) differential 2-form defined on a 2D differential manifold with coordinates ##\{x^{\mu}\}##. It can be assigned as linear combination...

Hi, Is the answer: y(x) _homogenous =v(x) y(x) _private =u(x)v(x) ? Or they refer to something else? I don't know how to approach to it

So I am a sophomore physics major at a university near my hometown. I have always been fascinated by the way studying physics makes me think about the world, and I have struggled with but enjoyed my other undergraduate physics and math classes. This semester, however, I am taking multivariable...

My question is, is this correct, and if so, why the minus sign?

Hi, I am looking at a Micsig DP2003 high voltage differential probe. It's rated for 5.6 kV differential voltage. I understand that the differential votlage is measuring across two terminals which can be floating (not referenced to GND). The specs say it is rated for 1 kV common mode voltage...

I am given this system of differential equations; $$ x_1'=2t^2x_1+3t^2x_2+t^5 $$ $$ x_2' =-2t^2x_1-3t^2x_2 +t^2 $$ Now the first question states the following; Find a fundamental matrix of the corresponding homogeneous system and explain exactly how you arrive at independent solutions And the...

Hello! Consider this ODE; $$ x' = sin(t) (x+2) $$ with initial conditions x(0) = 1; Now I've solved it and according to wolfram alpha it is correct (I got the homogenous and the particular solution) $$ x = c * e^{-cos(t)} -2 $$ and now I wanted to plug in the initial conditions and this is...

hi, i am working on nonlinear differential equation- i know rules which decide the equation to be nonlinear - but i want an answer by which i can satisfy a lay man that why the word nonlinear is used. it is easy to explain nonlinearity in case of simple equation i.e when output is not...

A ##\frac{df}{dx}## notation is problematic. Obviously, the letter 'd' has very different meaning when applied to the function or to the argument. Additionally, a separate letter '##\partial##' is used to denote a partial differential (a very rare case in math when a notation used for a general...

Hello! First I tried modelling it like most mixing problems. $$ \frac{dA}{dt} = rate coming in - rate coming out $$ where dA is the volume and dt is the time rate coming in/out can be describe as; contrencation * flow rate. Now if we plug that all on $$ \frac{dA}{dt} = 35 * 0 -...

Problem statement: Second order linear differential equation in standard from Reasoning:

$s=c_1*\exp(-c_2*|(t)|)*r(t)$ But how can I solve $c_1+c_2$ ?