Differential Definition and 1000 Threads

Homework Statement $$y'=-\frac{1}{10}y+(cos t)y^2$$ when doing substitute for ##z=\frac{1}{y}## I understand this is ##z(t)=\frac{1}{y(t)}## I know t is independent variable and y is dependent variable but I want to know what is z role here, is it change the dependent variable? when...

Homework Statement In my physics homework, I ran into a differential equation. I am attempting to solve this differential equation for y(x). Homework Equations y''[x] = -C/(y[x]^3) - y[x] C is a constant The Attempt at a Solution dy^2/dx^2 = -C y[x]^-3 - y[x] (1)/(-Cy[x]^-3 - y[x]) dy^2=...

Hi, I have a masters in physics but it is decades old and I am a little rusty. Plus, I didn't study calculus and differential equations carefully or systematically, as I was young and arrogant (not to say that all young people are arrogant, but I was). Returning to physics now, I find that I can...

Dear Everybody, I have a question about an example: "Solve the system: $x'(t)=3x(t)-4y(t)+1$ $y'(t)=4x(t)-7y(t)+10t$ We write the system using the operator notation: $(D-3)[x]+4y=1$ $-4x+(D+7)[y]=10t$ We can eliminate x from this system by adding 4 times the first equation to $(D-3)$...

I'm so confused about this question :(

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on Rn" I need some help with an aspect of Theorem 9.2.1 ... Theorem 9.2.1 reads as follows: Theorem 9.2.1 refers to and relies on Theorem 9.1.10 ... ... so I am...

Homework Statement I’m studying orthogonal curvilinear coordinates and practice calculating differential operators. However, I’ve run across an exercise where the coordinate system is only in 2D and I’m confused about how to proceed with the calculations. Homework Equations A point in the...

Hello! Currently I own Differential Equations by H.B Phillips, a really old book, but difficult and does it´s purpose. I have only 1 problem, certain exercises require certain geometrical functional study I suppose, for example: "find the equation of the curves so that the part of every tangent...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n" ... ... I need some help with another aspect of Definition 9.1.3 ... Definition 9.1.3 and the relevant accompanying text read as follows...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##" ... ... I need some help with another aspect of Definition 9.1.3 ... Definition 9.1.3 and the relevant accompanying text read as follows: In the...

Hi! I've been stuck on this problem for 2 days. I'm new here and I've just spent another hour on trying to figure out Latex, but it always ends up in a mess so I'll try without. I hope that's okay. The equation is y''+6y'+9y=4e-x with the value boundaries (I think that's what it's called in...

I've been trying to get a meaningful understanding of the benefits of using differential forms. I've seen examples of physics formulas that are reduced to a very simple declarative form relative to their tensor counterparts. However to me it just seems like a notation change to implied tensor...

I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an aspect of Kantorovitz's Example 3 on pages 65-66 ... Kantorovitz's Example 3 on pages 65-66 reads as follows...

I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an aspect of Kantorovitz's Example 3 on pages 65-66 ... Kantorovitz's Example 3 on pages 65-66 reads as follows: In the above example, we read...

Homework Statement Find the general solution of the given differential equation. Give the largest interval I over which the interval is defined.Determine wether there are any transient terms in the general solution 5. \frac {dy}{dx} + 3x^2y = x^2 Homework EquationsThe Attempt at a Solution...

Hello, I am studying control theory. And I have encountered something I have never considered or thought about. Consider a system with y as the output differential equation and u as the input. any(n) + ... + a1y(1) + a0y = bmu(m) + ... + b1u(1) + b0u Here, the subscripts indicate...

Hi all, so I'm not sure if what I'm asking is trivial or interesting, but is there any general or canonical way to interpret say, The follwing operator? (Specifically in the study of quantum mechanics): A = 1/(d/dx) (I do not mean d-1/dx-1, which is the antiderivative operator ) How would...

Homework Statement Given the following figure and the following variables and parameters, I have been able to come up with the set of differential equation below the image. My question is how does the system of equations 1 which I produced myself differ from the set of equations 2. Below I have...

Homework Statement Given the following figure and the following variables and parameters, I have been able to come up with the set of differential equation below the image. My question is how does the system of equations 1 which I produced myself differ from the set of equations 2. Below I have...

Homework Statement [/B] dy/dt = c - ky Homework Equations integral 1/y dy = ln(y) The Attempt at a Solution let y = c/k + z dy/dt = dz/dt = -kz dz/z = -kdt ln(z) = - kt z = e^(-kt) but z = y - c/k y = e^(-kt) + c/k + cons. answer should have been negative sign on the e term. I...

I was doing the calculations for this: http://fermi.la.asu.edu/PHY531/cylinder/index.html But I can't figure out how to go from \frac{d\sigma}{d\phi} to the total cross section. My guess was that you did the integral from \phi=0 to \phi=2\pi, but that's not helping since I can't tell either how...

Homework Statement $$y = x.\log_e {\sqrt{x}}$$ Homework Equations f(x) = g(x) h(x) f ' (x) = g ' (x) . h (x) - h ' (x) . g(x) The Attempt at a Solution $$y = x .\log_e {\sqrt {x}}$$ $$y '(x) = 1.ln \sqrt{x} + \frac{1}{2} $$ the right answer is $$ y ' = \log_{10} {\sqrt{x}} + \frac{1}{2} $$...

Hi PF! I'm reviewing a text and the author writes where ##g## is an arbitrary function and ##B## is a differential operator. ##Bo## is a parameter. Then the author states the inverse of ##B## is where ##G## is the Green's function of ##B##. Can someone explain how we know this?

How can I classify a given first order partial differential equations? Are all first order linear PDEs hyperbolic? Quora Link:https://www.quora.com/How-do-I-classify-first-order-PDE-elliptic-hyperbolic-or-parabolic-using-method-of-characteristics

Homework Statement Homework EquationsThe Attempt at a Solution For the homogeneous equation, I have got the the root of the characteristic equation as ## e^{ix}, e^{-ix} ## . So, the corresponding solution is ## B \sin{ x} + A \cos{ x} ## . Then, I took the particular solution as...

This is my college's description for it: Differential Geometry (3) Properties and fundamental geometric invariants of curves and surfaces in space; applications to the physical sciences. Pre: Calculus IV, and Introduction to Linear Algebra; or consent. I was doing pretty well in all my...

Problem: $${\frac {\partial }{\partial t}}A\left( y,t \right) +6\,\Lambda\,\Omega\, \left( {y}^{2}-y \right) \sin \left( t \right) ={\frac {\partial ^{2}}{\partial {y}^{2}}}A \left( y,t \right)$$ $${\frac{\partial }{\partial y}}A \left( t,0 \right) ={\frac {\partial }{\partial y}}A \left( t,1...

Homework Statement The question is Derive an expression for the closed loop gain of the differential amplifier. I have solutions for these questions but the solution for this question is quite vague. Here is the solution: I understand part 1 and part 3, but part 2 I don't. So looking at...

I saw this problem and solved it but still I had one question... Homework Statement A rock falls through water with a continuously decreasing acceleration. Assume that the rock’s acceleration as a function of velocity has the form ay = g - bvy where b is a positive constant. (The +y direction...

Homework Statement Suppose the acceleration of a particle is a function of x, where a(x)=(2.0 s-2)*x. (a) If the velocity is zero when x= 1.0 m, what is the speed when x=3.0 m? (b) How long does it take the particle to travel from x=1.0 m to x=3.0 m. a(x)=(2.0 s-2) * x (a) V(x=3) = ? , V(x=1)...

I feel so sorry when I found myself trapped in a basic problem like this one, but let's go ahead... Suppose we have the following equation, knowing that ##B## is a constant, $$\frac{dU( \theta)}{d \theta} + 2Br = 0$$ where we want to solve for ##B##. If we differentiate the above equation with...

So I've seen in several lectures and explanations the idea that when you have an equation containing a relation between certain expressions ##x## and ##y##, if the expression ##x## approaches 0 (and ##y## is scaled down accordingly) then any power of that expression bigger than 2 (##x^n## where...

Hello, I ran a test on an industrial composite of 30% glass-filled nylon 6, and my melting temperature peak is too low. The range was from -30 C to 275 C. Why could this be happening? Should I suspect the sample pan? Thanks.

I need to solve: \dot{\mathbf{r}}=-kv\hat{r} - \dot{\mathbf{r}_s} However, I do not know how to deal with the fact that there is a unit vector. How can this be done? \dot{\mathbf{r}_s} is a constant vector.

I'm reading up on the use of the valve seen in the link below. On page page 5-6 there is the mentioning of available differential pressure. I struggle with understanding what that means exactly. Say I have a set of main supply/return pipes along a building, with some branches along the way...

It would be wonderful if someone could please help with the following question as I don't even know where to begin y=y(x), where x^2 cos y + sin(3x-4y) =3Thank you :)

In How is equation 145 giving a direction(ie gradient) and not a slope?. Also here how is equation 147 arrived at? Any help would be much appreciated.

How is mass flow rate within an annular region of a pipe taken to be an inexact differential? I read it in Fluid Mechanics textbook by Yunus A. Cengel and John M. Cimbala. The mass flow rate through the annulus is given to be inexact differential. Why is mass flow through the annulus not equal...

Homework Statement y'+tanxy=sinx Homework Equations integrating factor I(x)= exp{lnIsecxI}[/B]The Attempt at a Solution I have secxy= integral of sinx I(x) I am not sure how to integrate that because secx is in absolute value form.[/B]

Hi, Below are the neutron flux spectra of a nuclear reactor. In the first spectrum, y-axis is differential flux and in the second spectrum, y-axis is flux (created by multiplying differential flux by energy in MeV). As far as I have seen so far, differential flux is used commonly. I am just...

Homework Statement Homework EquationsThe Attempt at a Solution Is there anyway to answer this question without solving the eqn and plotting the graph? The function will not oscillate as there is -4y on the right side. So, the first option gets canceled. Since there is a resistive part i.e...

First, some may ask why would do we care that we can convert a 3rd order or higher ODE into a system of equations? Well there are quite a few reasons. 1- Almost all first order systems are easier to solve numerically using computer systems (matlab, maple, etc). Yes, it takes some working out...

I tried using the Bernoulli equation to solve this. I took two points at the surface of the water in both the containers and formed this equation: gh_{b}=\frac{1}{2}v^2+gh This is assuming that the velocity of the water in the large tank is approximately zero and using the fact that both the...

Homework Statement [/B] Homework Equations Adiff(single-ended)= 1/2gm*ro||Rd β=R2/(R1+R2) The Attempt at a Solution I am really confused as to how to find A. I know the feedback of the circuits around the R2 and R1, but I don't understand how the open loop gain can be found. Can someone...

This is a small part of a question from the book, so I think the format does not really apply here. When doing questions for solving differential equation with substitution, I encountered a substitution ## y(x)=\frac{1}{v(x)} ##. And I am not sure about the calculus in finding ## \frac{dy}{dx}...

Hello, I need a quick clarification on how the differential works. I understand its purpose and how it operates but I am not sure how, when a car is turning, the spider gear starts spinning to provide the outer wheel with a higher angular velocity? Is it simply because the outer wheel starts to...

Homework Statement (also express C and alpha as functions of A and B) I need help with the second part (rewriting the solution). Homework Equations ejθ = cos(θ) + jsin(θ) The Attempt at a Solution Unfortunately, I can't think of how to even begin solving. I have the notion that I have...

Hello! I started reading some differential geometry applied in physics (wedge product, Hodge duality etc.) and how you can rewrite classical theories (Hamiltonian Mechanics, Electromagnetism) in a much nicer way. Can someone point me towards some reading about how can more information be...

Dear members, Do you maybe know some good reference for the application of differential geometric methods in biology, especially evolutionary theory, game theory, population ecology. I kinda feel that the application of mathematical methods in biology in general is a field of increasing...

Homework Statement I as just hoping someone could help me parse the notation here. What does the superscript "d" mean in the differential of the integral? Thanks!