Differential Definition and 1000 Threads

<Moderator's note: Moved from a technical forum and thus no template.> Is what I have done correct ? I want to find v(t) from Sigma F = m*a. I have gravity force mg pointing downward with positive direction and resistive force R = -b*v^2 pointing upwards with negative direction are acting on a...

The question provides the vector field (xy, 2yz, 3zx) and asks me to confirm Stokes' theorem (the vector calc version) but I am trying to use the generalized differential forms version. So, I am trying to integrate \omega = xy\,dx + 2yz\,dy + 3zx\,dz along the following triangular boundary...

Homework Statement If a = 9-v² then prove that v = 3 (e^6t - 1)/(e^6t + 1) the condition when t=0 also v has zero value Homework Equations I don't quite understand in this but general equation should be dv/dt = a The Attempt at a Solution Actually i don't don't have any idea in this problem...

O'Neill's Elementary Differential Geometry contains an argument for the following proposition: "Let C be a curve in a plane P and let A be a line that does not meet C. When this *profile curve* C is revolved around the axis A, it sweeps out a surface of revolution M." For simplicity, he...

Hey, this is how i tried solving the differential equation The solution however does not match the general solution of the equation. Also differentiating it twice does not give me the previous equation. Please tell me if i did some mistake while solving. I already know how to solve by finding...

Hi I have always had an issue with understanding the definitions used in mathematics. I need examples before I can start using and reasoning with them. However, with tensor products, I have been completely stuck. Stillwell's Elements of Algebra was that made abstract algebra "click" for me...

Hi! I'm asked to find all the non-zero Christoffel symbols given the following line element: ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy The result I have obtained is that the only non-zero component of the Christoffel symbols is: \Gamma^x_{xx}=\frac{1}{x} Is this correct? MY PROCEDURE HAS BEEN: the...

Hello. I am studying Analysis on Manifolds by Munkres. My aim is to be able to study by myself Spivak's Differential Geometry books. The problems is that the proof in Analysis on Manifolds seem many times difficult to understand and I am having SERIOUS trouble picturing myself coming up with...

Hi, I'm attempting to learn differential equations on my own. Does anyone recommended a textbook that comes with/has a solution manual? I learn faster when I can see a problem worked out if I can't solve it. Thanks.

Homework Statement Solve the following differential equations/initial value problems: (cosx) y' + (sinx) y = sin2x Homework Equations I've been attempting to use the trig ID sin2x = 2sinxcosx. I am also trying to solve this problem by using p(x)/P(x) and Q(x) The Attempt at a Solution...

Homework Statement Solve the following differential equations/initial value problem: y^(4) - y'' - 2y' +2y = 0 Hint: e^-x sinx is a solution Homework Equations I was attempting to solve this problem by using a characteristic equation. The Attempt at a Solution y'''' -y'' -2y' + 2y = 0 -->...

Suppose we have the matrix $ \mathbf{N} = \begin{bmatrix} 4 & -2 \\ -2 & 1 \end{bmatrix}$ and $\mathbf{X} = \begin{bmatrix}x \\ y \end{bmatrix}$. I want to solve $\displaystyle \frac{d\mathbf{X}}{dt} = \mathbf{NX}$. The eigenvalues of the matrix are $\lambda_1, \lambda_2 = 0,5$ and eigenvectors...

Hello, could someone please give me some examples of where order linear non homogenous ordinary differential equations are used in physics[emoji4]

Hello! I just start looking at SDG and I'm already having difficulties with a few concepts as expressed by A Kock as: "We denote the line, with its commutative ring structure (relative to some fixed choice of 0 and 1) by the letter R" "The geometric line can, as soon as one chooses two...

Dear all I've been trying to work out the general solution to a 2nd order ODE of the form f''(x)+p(x)*f(x)=0 p(x) is a polynomial for my case. I believe series method should work, but for some reason I would prefer a general solution using other methods. I'll be much appreciative for any help...

Find the general solution of the given differential equation $\displaystyle y^\prime - 2y = t^2 e^{2t}$ Obtain $u(t)$ $\displaystyle u(t)=\exp\int -2 \, dx =e^{-2t}$ Multiply thru with $e^{-2t}$ $e^{-2t}y^\prime + 2e^{-2t}y = t^2 $ Simplify: $(e^{-2t}y)'= t^2$...

Hi all! I was messing around with the equation for time dilation. What I wanted to do was see how the time of a moving observer ##t'## changed with respect to the time of a stationary observer ##t##. So I differentiated the equation for time dilation ##t'## with respect to ##t##: $$\frac {dt'}...

$\textsf{ Verify the following given functions is a solution of the differential equation}\\ \\$ $y''''+4y'''+3y=t\\$ $y_1(t)=t/3$ \begin{align*} (t/3)''''+4(t/3)'''+(t/3)&=t\\ 0+0+t&=t \end{align*} $y_2(t)=e^{-t}+t/3$ \begin{align*} (e^{-t}+t/3)''''+4(e^{-t}+t/3)'''+3(e^{-t}+t/3)&=t\\...

Hi, This is a NEW method for solving differential equations - Case Studies. Please go to this website to see how: http://www.sysins.com Thanks. Yousif Sammour.

Hello all, I want to say thank you in advance for any and all advice on my question. My classical mechanics textbook (Marion Thornton) has been taking me through motion for a particle with retarding forces. The example it keeps giving is: m dv/dt = -kmv which can be solved for: v = v0e-kt...

I am aware that hypergeometric type differential equations of the type: can be solved e.g. by means of Mellin transforms when σ(s) is at most a 2nd-degree polynomial and τ(s) is at most 1st-degree, and λ is a constant. I'm trying to reproduce the method for the case where λ is not constant...

I am asked to solve the differential equation $$ f''(\eta)+\frac{f'(\eta)}{\eta}+\Big(1-\frac{s^2}{\eta^2}\Big) f(\eta) - f(\eta)^3 = 0, $$ for small ##\eta## and large ##\eta## under the condition ##f(\eta \rightarrow \infty) = 1## and ##f(0)=0##. The numerically solved solution looks like...

I have seen how to solve the heat equation: $$ \frac{ \partial^2 u(x,t) }{\partial x^2} = k^2 \frac{ \partial u(x,t) }{\partial t} $$ With boundary conditions. I use separation variables to find the result, but i don't know how to solve the equation plus a...

<Moderator's note: Moved from a technical forum and thus no template.> Hi everyone, I have encountered a partial differential equation with square roots which I don't have a clue in solving it. After letting z=F(x)+G(y), I can't really figure out the next step. I tried squaring both sides but...

Hi, I was trying to solve the simplest problem of planetary motion (for one planet). The equations should be: ##F_x = m \frac {d^2x} {dt^2} = G \frac {Mmx} {r^3}## ##F_y = m \frac {d^2y} {dt^2} = G \frac {Mmy} {r^3}## where ## r = \sqrt{x^2 + y^2}## So I re-wrote the system like this...

1. The problem statement, all variables, and given/known data Task requires you to solve a partial differential equation $$u_{xy}=2yu_x$$ for ##u(x,y)##. A hint is given that a partial differential equation can be solved in terms of ordinary differential equations. According to the solution...

I am reading Griffiths' Introduction to Quantum Mechanics, specifically the chapter on scattering. He is discussing the scenario where an incoming beam of particles scatter off an azimuthally symmetric target. At large separation ##r## from the scattering centre, the wavefunction for incoming...

Can all differential equations be turned into algebraic equations by Fourier transform (FT)? If not, what kind of differential equations can be solved by the FT technique?

I tried to convert the second order ordinary differential equation to a system of first order differential equations and to write it in a matrix form. I took it from the book by LM Hocking on (Optimal control). What did I do wrong in this attachment because mine differs from the book?. I've...

Homework Statement Homework EquationsThe Attempt at a Solution I managed to find dy/dx as follows: But I'm having difficulty finding the second derivative. I've looked at examples using the chain rule but I'm still confused. Would someone mind shedding some light on this for me?

Hi guys, I have encountered a problem in fluid mechanics that gives a three-dimensional vector differential equation \begin{equation} a \vec{f} + \nabla{a} + b \nabla{c} = \vec{0} \end{equation} where a, b, and c are unknown scalar functions of three-dimensional space and f is a known vector...

Mixing with a Common Drain. Two tanks, each holding 1 L of liquid, are connected by a pipe through which liquid flows from tank A into tank B at a rate of 3-a L/min (0<a<3). The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 3 L/min. Solution flows out of...

Homework Statement I have derived the differential equations of a system. They are like the following: a\ddot{\theta} - b\ddot{x} + c \theta = 0 \\ d\ddot{\theta} + e\ddot{x} = F(t) where a,b,c,d,e are constants. I'm having trouble putting it into state space form, since I have the highest...

a) y'' + 3y' - y = 3sin3x This is not homogeneous. b) y'' + 3y' - y = 0 This is homogeneous. I see b) is homogeneous because it equals to 0. What are further conclusions for that. How we can predict particular solution in a) to be: y = Asin3x + Bcos3x? And how to predict solutions for other...

Homework Statement Consider interactions of a X-ray beam at a depth, x, within a material. The flux density is: density flux = $$\frac{I}{A}$$ where I is the intensity of the beam that cross a unit area A at right angles to the beam. Let dx be a small slice at the depth x and let dI(x) be the...

Hello, does anyone know an (more or less) easy differential geometry book for courses in generall relativity and quantum field theory? I'm looking for a book without proofs that focus on how to do calculations and also gives some geometrical intuition. I already looked at The Geometry of...

i have used series solutions to differential equations many times but i never really stopped to think why it works i understand that the series solution approximates the solution at a local provided there is no singularity in which frobenius is used but i am not understanding how exactly it...

Homework Statement Solve ##\frac{dy}{dt} -y = 1, y(0) = 0## using the laplace transform Homework EquationsThe Attempt at a Solution ##\mathcal{L}\big\{\frac{dy}{dt}\big\} - \mathcal{L}\big\{y\big\} = \mathcal{L}\big\{1\big\}## ##sY(s) - y(0) - \frac{1}{s^2} = \frac{1}{s}## ##Y(s)...

Homework Statement I was never great in diffEQ, but now I have to solve this problem for physics homework and I'm pretty lost. d^4x/dx^4 - d^2x/dx^2 + a =0 Where a is a parameter.Homework EquationsThe Attempt at a Solution I have tried solutions like e^kt which work accept for the parameter...

Homework Statement A submarine of mass 80 000 kg is floating at rest (neutrally buoyant) at a depth of 200 m in sea water. It starts pumping out sea water from its ballast tanks at a rate of 600 litres per minute, thus affecting both its mass and the buoyancy force. Determine the vertical...

Hi. Can anyone recommend a text introducing differential forms along with all the necessary pre-requisites for understanding them? For example, I'm not really familiar with tensor calculus but would like to shortcut studying it completely separately to learning differential forms. If that's too...

I have a first order bernoullis differential equation. I need to solve this in matlab. Can anyone help me?

Homework Statement Finding the general solution: y”+4y’+4y=t*e^(-2t) Homework EquationsThe Attempt at a Solution So I got the complementary solution pretty easily as y= c1*e^(-2t)+c2*te^(-2t) I haven’t been able to find a particular solution using the method of undetermined coefficients. I...

Question - True or False: If $\frac{dx}{dt}$ = $\frac{1}{x}$ and $x$ = 3 when $t$ = 0, then $x$ is an increasing function of $t$. I understand how the graph of $x$ was obtained (the graph on the board), but I really don't understand why she attempted to draw the negative root of $x$ the way...

Homework Statement Homework Equations Power series The Attempt at a Solution As I have to write in form of "x^2n" & "x^2n+1", I am totally have no idea with how can I go on to do the question. Those I have learned in lecture and online are mostly with only one part of summation... or two...

Hy folks, Upfront I want to apologize for my writing and my dissability to use correct symbols to ease readability of the example. Ok now that that's done I just want to start upfront. If we set a usual example of an object falling from a tower with a height of x meters and assume that the...

Homework Statement Hello. I'm trying to do some problem and I can't solve some differential equation from the 2nd degree: X'' - (F0 / ( d * m)) * X = 0 d, m, F are constant that are known Homework Equations I know that solution is a trigonometry equation. But I want to see how to solve...

Hi PF, initially I would like you to focus on that link https://books.google.com.tr/books?id=Dkp6CwAAQBAJ&pg=PA389&lpg=PA389&dq=runge+kutta+method++is+tvd+proof&source=bl&ots=47ULQDVwcC&sig=e2zjdnXENJ7WxBbrf6hXkSouvLI&hl=tr&sa=X&ved=0ahUKEwjU5Z2XsbXZAhUMCMAKHWpnATQ4ChDoAQhKMAQ#v=onepage&q=runge...

Homework Statement I am working through problem #1, a-c. Homework Equations The main equations are dx/dt=Ax, (A-rI)v=0, and det(A-rI)=0. The Attempt at a Solution [/B] Here is my attempt. I am fairly confident in my answer to A. I'm less sure on my answer to B, however it is the same as...

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...