Differential Definition and 1000 Threads

ial this is the question.

>10. Let a family of curves be integral curves of a differential equation ##y^{\prime}=f(x, y) .## Let a second family have the property that at each point ##P=(x, y)## the angle from the curve of the first family through ##P## to the curve of the second family through ##P## is ##\alpha .## Show...

I have my set of differential equations which is dx/dt = -2x, dy/dt=-y+x2, with the initial conditions x(0)=x0 and y(0)=y0. I'm a little confused about how to approach this problem. I thought at first I would differentiate both sides of dx/dt = -2x in order to get d2x/dt2 = -2, and then I would...

the differential equation that describes a damped Harmonic oscillator is: $$\ddot x + 2\gamma \dot x + {\omega}^2x = 0$$ where ##\gamma## and ##\omega## are constants. we can solve this homogeneous linear differential equation by guessing ##x(t) = Ae^{\alpha t}## from which we get the condition...

That's pretty much it. If there is a very basic strategy that I am forgetting from ODEs, please let me know, though I don't recall any strategies for nonlinear second order equations. I've tried looking up "motion of a free falling object" with various specifications to try to get the solution...

Well, I followed the strategy used by A.S. Parnovsky in his article (\url{http://info.ifpan.edu.pl/firststep/aw-works/fsV/parnovsky/parnovsky.pdf}) and found this differential equation: $$-\frac{g x}{C^{2}} = -\frac{\beta^{2} {y^{\prime}}^{2} \arctan\left({y^{\prime}}\right) + \beta...

The first two parts I think were fine, I expressed the tensors in coordinate basis and wrote for the first part$$ \begin{align*} \mathcal{L}_X \omega = \mathcal{L}_X(\omega_{\nu} dx^{\nu} ) &= (\mathcal{L}_X \omega_{\nu}) dx^{\nu} + \omega_{\nu} (\mathcal{L}_X dx^{\nu}) \\ &= X^{\sigma}...

Good Morning To cut the chase, what is the dx in an integral? I understand that d/dx is an "operator" on a function; and that one should never split, say, df, from dx in df/dx That said, I have seen it in an integral, specifically for calculating work. I do understand the idea of...

Summary:: We want to find explicit functions ##g(y,t)## and ##f(y,t)## satisfying the following system of differential equations. I attached a very similar solved example. Given the following system of differential equations (assuming ##y \neq 0##) \begin{equation*} -y\partial_t \left(...

Hi all, if anyone could help me solve this 2nd order differential equation, it would mean a lot. Problem: Solve the equation with y = 1, y' = 0 at t = 0 y'' - ((y')^2)/y + (2(y')^2)/y^2 - ((y')^4)/y^4 = 0 I have never solved an ODE of this kind before and I am not sure where to start...

I would to know if I'm solving system differential equation by elimination correctly. Could somebody check my sample task and tell if something is wrong?

I got to know of this book through Freeman Dyson's obituary. Just wondering, is it useful in studying Physics (it seems to cover everything), do people even use it these days? I understand differential equations are basically half of Physics. By the way, this book is really old, are there any...

I have the solution to the problem, and I mechanically, but not theoretically (basically, why do the C(s) and R(s) disappear?), understand how we go from ##(s^5 + 3s^4 + 2s^3 + 4s^2 + 5s + 2) C(s) = (s^4 + 2s^3 + 5s^2 + s + 1) R(s)## to ##c^{(5)}(t) + 3c^{(4)}(t) + 2c^{(3)}(t) + 4c^{(2)}(t) +...

Hello, I would like to is it possible to solve such a differential equation (I would like to know the z(x) function): \displaystyle{ \frac{z}{z+dz}= \frac{(x+dx)d(x+dx)}{xdx}} I separated variables z,x to integrate it some way. Then I would get this z(x) function. My idea is to find such...

Hi there can someone please help me with this differential equation, I'm having trouble solving it $$ \begin{cases} y''(t)=-\frac{y(t)}{||y(t)||^3} \ , \forall t >0 \\ y(0)= \Big(\begin{matrix} 1\\0\end{matrix} \Big) \ \text{and} \ y'(0)= \Big(\begin{matrix} 0\\1\end{matrix} \Big)\end{cases}...

I am confused as to how exactly we integrate differential forms. I know how to integrate them in the sense that I can perform the computations and I can prove statements, but I don't understand how it makes sense. Let's integrate a 1-form over a curve for example: Let ##M## be a smooth...

I am test my knowledge of differential forms and obviously I am missing something because I can't figure out where I am going wrong here: Let ##C## denote the positively oriented half-circle of radius ##r## parametrized by ##(x,y) = (r \cos t, r \sin t)## for ##t \in (0, \pi)##. The value of...

I tried it but I don't know how to evaluate the integral on the last equation. Help.

I have three differential equations with three unknowns ##p##, ##q## and ##r##: $$\displaystyle {\frac {\partial }{\partial p}}\sum _{k=1}^{5}f_{{k}}\ln \left( P \left( X=k \right) \right) =0$$, $$\displaystyle {\frac {\partial }{\partial q}}\sum _{k=1}^{5}f_{{k}}\ln \left( P \left( X=k...

The first equation leads to x = ae^2t + be^t and the second equation leads to y=[1/(ln(sint+pi/2)+c)] this corresponds to the system a+b=1/c 2a+b=1 which has infinitely many solutions. what am I missing here?

I'm confused at the part how 4Vc and 48 cos(60t) are deduced, that's all.

$\tiny{27.1}$ 623 Find a general solution to the system of differential equations $\begin{array}{llrr}\displaystyle \textit{given} &y'_1=\ \ y_1+2y_2\\ &y'_2=3y_1+2y_2\\ \textit{solving } &A=\begin{pmatrix}1 &2\\3 &2\end{pmatrix}\\...

##-\frac {dy}{dx}=\frac {3+4v}{4-3v}## ##\frac {3+4v}{4-3v}=-v-x\frac {dv}{dx}## ##-\frac {dx}{x}=\frac {4-3v}{8v-3v^2+3}## ##\frac {dx}{x}=\frac {4-3v}{3v^2-8v-3}##=[A/3v+1]+[B/v-3]##

Not sure how to start off this question I'm confused how to begin if I do not the exact pressure on either pipe A or pipe B Only thing that I can deduce from this is that if pipe A exerts a smaller pressure than before then the mercury column on the left side would rise i.e. the new...

Greetings everyone, I am a bit new to differential equations and I am trying to solve for the natural and forced response of this equation: dx/dt+4x=2sin(3t) ; x(0)=0 Now I know that for the natural response I set the right side of the equation equal to 0, so I get dx/dt+4x=0, thus the...

Today the inexact differential is usually denoted with δ, but in a text by a Russian author I found a dyet (D-with stroke, crossed-D) instead: In response to my question to the author about this deviation from normal usage, he stated that this was a suggestion from von Neumann. (Which of course...

Hello everyone! I was studying chaotic systems and therefore made some computer simulations in python. I simulated the driven damped anhatmonic oscillator. The problem I am facing is with solving the differential equation for t=0s-200s. I used numpy.linspace(0,200,timesteps) for generate a time...

Data: The speed of right wheel is considered to be 25 RPM. The speed of left wheel is considered to be 20 RPM. The distance, L, between wheels is 30 cm. Also the radius, r, of each wheel is 6 cm. Question: Using the data above for a differential robot, find the following: i: angular...

Differentiating eq1 mentioned above, and using eq 2, i got : $$v\frac{dv}{d\theta}=R\frac{dv}{dt}$$ From this, i got:$$ \frac{d\theta}{dt}=\sqrt{(2/R)(g(1-cos\theta )+asin\theta)}$$ After this point, I am not able to understand what substitution or may be other method could be used to solve...

I'm reading 'Core Principles of Special and General Relativity' by Luscombe - the part on parallel transport. I guess ##U^{\beta}## and ##v## are vector fields instead of vectors as claimed in the quote. Till here I can understand, but then it's written: I want to clarify my understanding of...

I know the solution to the equation (1) below can be written in terms of exponential functions or sin and cos as in (2). But I can't remember exactly how to get there using separation of variables. If I separate the quotient on the left and bring a Psi across, aka separation of variables (as I...

We choose an approximative solution given by $$ u_N(x) = \frac{a_0}{2} + \sum_{n=1}^N a_n \cos nx + b_n \sin nx $$ Comparing this approximative solution with the differential equation yields that $$ \frac{a_0}{2} = a $$ and the boundary conditions yields the equation system $$ a + \sum_{n=1}^N...

One thing that is given in paper (attached) is a operating set point for temperature which is given as 20 for day and 16 for night but I do not know whether its initial condition for temperature or not. Can anyone please guide me that what kind of equation is it and how can I solve it with these...

Hi folks, My understanding of the Compton Effect is that maximum energy transfer to the electron takes place when the photon scattering angle is 180 degrees. For the following please reference Evans "The Atomic Nucleus" ...

I am reading A Course in Mathematical Analysis Volume 1 by D. J. H. Garling, and I am having trouble in the following demonstration of Section 2 Differentiation. part 4 of the test, the first part of the second inequality does not make sense, I do not understand its justification. I hoped they...

looking for some assistance working out torque equations for this set-up please.

$$p=\gamma m v$$ $$F = \frac {md (\gamma v}{dt}$$ $$\int{F dt} = \int{md (\gamma v}$$ $$F t= \gamma mv$$ At this step, I don't know how to make v as explicit function of t, since gamma is a function of v too. Thankss

I read in the book Gravitation by Wheeler that "Any tensor can be completely symmetrized or antisymmetrized with an appropriate linear combination of itself and it's transpose (see page 83; also this is an exercise on page 86 Exercise 3.12). And in Topology, Geometry and Physics by Michio...

Could you provide recommendations for a good modern introductory textbook on differential geometry, geared towards physicists. I know physicists and mathematicians do mathematics differently and I would like to see how it is done by a physicists standard. I have heard Chris Ishams “Modern Diff...

Fluid can exert force to object(move object) only through pressure and tangential stress caused by viscosity. if we look at balloon rocket ,here is Newton 3 law action-reaction,but this 3 law as usual don't tell nothing how fluid really exert force to the ballon.. it exert through pressure...

I use the operator method here: (D^2 + D+3)y = 5cos(2x+3) ## y = \frac{1}{D^2+D+3} 5cos(2x+3) ## ## \Rightarrow y= \frac{5}{-(2)^2+D+3}cos(2x+3) ## ## \Rightarrow y= \frac{5}{-4+D+3}cos(2x+3) ## ## \Rightarrow y= \frac{5}{D-1}cos(2x+3) ## At this, if I revert back to write: (D-1)y = 5cos(2x+3)...

Here is my attempt at a solution: y = f(x) yp - ym = dy/dx(xp-xm) ym = 0 yp = dy/dx(xp-xm) xm=ypdy/dx + xm xm is midpoint of OT xm = (ypdy/dx + xm) /2 Not sure where to go from there because the solution from the link uses with the midpoint of the points A and B intersecting the x-axis...

So in particular, how could the determinant of some general "operator" like $$ \begin{pmatrix} f(x) & \frac{d}{dx} \\ \frac{d}{dx} & g(x) \end{pmatrix} $$ with appropriate boundary conditions (especially fixed BC), be computed? And assuming that it diverges, would it be valid in a stationary...

Summary:: Differential amplifier common mode gain derivation of forumlas I'm having a hard time deriving for equations 10-8 -10-9. I tried adding equation's 18-6 and 18-7 but cannot proceed with the derivation. I need help on this. Thank you!

Good Morning Recently, I asked why there must be two possible solutions to a second order differential equation. I was very happy with the discussion and learned a lot -- thank you. In it, someone wrote: " It is a theorem in mathematics that the set of all functions that are solutions of a...

Im unsure if I am on the correct track or have gone off on a tangent. Any help or guidance would be appreciated. CMRR=20log10(Adiff/Acm) 120=20log10(10^5/Acm) 120/20=log10(100,000/Acm) 6=log10(100,000/Acm) taking antilogs 1,000,000=100,000/Acm Acm=100,000/1,000,000 Acm=0.1Max amplified...

I'm reading a text on special relativity (Core Principles of Special and General Relativity), in which we start with the equation for composition of velocities in non-standard configuration. Frame ##S'## velocity w.r.t. ##S## is ##\vec v##, and the velocity of some particle in ##S'## is ##\vec...

There are a few different textbooks out there on differential geometry geared towards physics applications and also theoretical physics books which use a geometric approach. Yet they use different approaches sometimes. For example kip thrones book “modern classical physics” uses a tensor...

Hi, I really struggled to dig valuable things out of internet and books related to high order homogeneous differential equation with variable coefficients but I have nothing. All methods I see involves given solution and try to find others(like reduction of order method), even for second order...

\begin{equation} y_{1}{}'=y_1{}+y_{2} \end{equation} \begin{equation} y_{2}{}'=y_2{}+u \end{equation} build a control \begin{equation} u \epsilon L^{2} (0,1) \end{equation} for the care of the appropriate system solution \begin{equation} y_{1}(0)=y_{2}(0)=0 \end{equation} satisfy...