Differential Definition and 1000 Threads

  1. A

    Finding Solutions to Differential Equations with Constant Coefficients

    What is the general method for solving a differential equation of the form \begin{equation} \frac{\partial^{2}z}{\partial x^{2}}+\frac{\partial^{2}z}{\partial y\partial x}=C\end{equation} where C is a constant.
  2. N

    Differential equation (cannot separate)

    Homework Statement Solve for y using the substitution: z = 1/(y^5) dy/dx + y/x = (y^6)(x^3) Homework Equations (dz/dx) = (dz/dy) x (dy/dx) The Attempt at a Solution I formed an equation for dz/dx but cannot separate the variables in order to integrate. Can someone tell me where I've gone...
  3. P

    Hodge duality and differential forms

    If we have,$$A=d[(\bar{\alpha}-\alpha)(dt+\lambda)]$$ where $$\alpha$$ is a complex function and $$\lambda$$ is a 1-form. t here represents the time coordinate. If we want to calculate $$d\star A=0$$ where $$\star$$ is hodge star, we get if I did my calculations correctly...
  4. S

    Find the best T(t) from a differential eq. and conditions

    An electric vehicle of mass ##m## moves along the ##0-x## axis according to the law: m\frac{\mathrm{d} v(t)}{\mathrm{d} t} = T(t)-\mu mg-kv(t)^{2} (ma = Thrust - Friction - Drag) It is known that: P(t) = T(t)v(t) (Power = Thrust * Speed) Find the thrust ##T(t)## in such a way that the...
  5. E

    Vector differential identity proof (using triple product)

    Homework Statement Need to prove that: (v⋅∇)v=(1/2)∇(v⋅v)+(∇×v)×v Homework Equations Vector triple product (a×b)×c=-(c⋅b)a+(c⋅a)b The Attempt at a Solution I know I could prove that simply by applying definitions directly to both sides. I haven't done that because that is tedious, and I...
  6. N

    Help finishing a linear differential equation. Mechanics

    Homework Statement Find the distance which an object moves in time t if it starts from rest and has an acceleration d^2x/dt^2 = ge^-kt. Show that for small t the result is approx "x=(gt^2)/2" and show that for very large t, the speed is approximately constant. the constant is called the...
  7. M

    MHB Differential equation - Green's Theorem

    Hey! :o I want to find the solution of the following initial value problem: $$u_{tt}(x, t)-u_{xt}(x, t)=f(x, t), x \in \mathbb{R}, t>0 \\ u(x, 0)=0, x \in \mathbb{R} \\ u_t(x, 0)=0, x \in \mathbb{R}$$ using Green's theorem but I got stuck... I found the following example in my notes...
  8. B

    How to Show the Wronskian of Three Distinct Solutions Equals Zero?

    Homework Statement Hello, I was just looking for a quick tip: If I have three distinct solutions to a second order linear homogeneous d.e, how would I show that the wronskian of (y1,y2,y3)(x)=0? I know how to show the wronskian is not zero for a linearly independent set, but I'm confused...
  9. D

    What is the interpretation of dx in calculus?

    Apologies if this isn't quite the right forum to post this in, but I was unsure between this and the calculus forum. Something that has always bothered me since first learning calculus is how to interpret dx, essentially, what does it "mean"? I understand that it doesn't make sense to consider...
  10. J

    Expressing the equation of hydrostatic equilibrium

    Homework Statement This problem has been stumping me for days now, I'm sure I'm missing something simple as it's only worth a small number of marks on the coursework. Any help would be appreciated. I've been asked to re-express the equation of hydrostatic equilibrium: dP/dr = - Gm/4πr4...
  11. B

    Is My Solution for a Non Homogeneous D.E. with Given Initial Conditions Valid?

    Homework Statement hello all, Suppose y is a solution of the d.e: y"+p(x)y'+q(x)y= q(x) on the interval (-1,1) with y(0)=1 and y'(0)= 1. What is y? Homework Equations I used the auxiliary equation: m^2+p(x)m+q(x)= q(x) The Attempt at a Solution My question is can I do this? I can cancel...
  12. U

    Do i need differential equations?

    A friend recently gave me a book on quantum mechanics. It's called Introduction to quantum mechanics. It's by David j griffiths. I am currently taking multivariable calc.I am taking linear algebra next semester. I want study this book, but I am wondering what mathi I need. My friend told me I...
  13. Paradox101

    Radial Eigenfunction; Differential Equation

    Homework Statement Show that the radial eigenfunction unr,l is a solution of the differential equation: ħ2/2me×d2unr,l/dr2+[l(l+1)ħ2/2mer2 - e2/4πε0r]unr,l=Enr,lunr,lHomework Equations The radial function is R(r)=u(r)/r, so that the expression on the RHS is E×u. The Attempt at a Solution I know...
  14. T

    Help with First Order Differential

    Homework Statement The Attempt at a Solution The first part is fairly simple I think. It's just rate of accumulation = rate of generation - rate of output(losses) I'm not too sure how to solve this differential equation. I divide the whole equation through by mc and rearrange but I keep...
  15. patrickbotros

    Absolute Values in Separable Differential Equations

    When solving a separable differential equation, my textbook says this: ln|v-49|=-t/5+C→ |v-49|=e-t/5+C→ v=49+ce-t/5 What happened to the absolute values? I think it has something to do with the exponential always being positive.
  16. M

    How Can I Use the Slope Field Method to Solve a Differential Equation?

    Homework Statement dy/dx=2xcos(y)-xy^3[/B]Homework EquationsThe Attempt at a Solution dy/dx=2xcos(y)-xy^3=x(2cosy-y^3) dy/(2cosy-y^3)=xdx [/B] I can not integrate the left side of the equation. Can someone help me please?
  17. M

    Ordinary or partial differential equation

    Homework Statement x(d^2y/dx^2)+dx/dt+xy=0 Homework EquationsThe Attempt at a Solution At first I thought it was an ODE, but then I found out the derivative was respect to to variables x and t. I am not sure if it is an ODE or PDE. What are the dependent and independent variables in the...
  18. U

    2-form oriented triangle, Differential Forms

    Homework Statement Find the value of the 2-form dxdy+3dxdz on the oriented triangle with (0,0,0) (1,2,3) (1,4,0) in that order. Homework EquationsThe Attempt at a Solution I have tried various subtraction of these coordinates and applying them to the formula but the answer is in the back of...
  19. D

    Does the gear ratio in a differential affect pitching loads

    I'm designing a differential mount and am trying to wrap my head around the pitch loads the mount sees. My question is with a 1000 Ft/lb input torque will the ring and pinion ratio effect the torque that the mount must resolve? The differential is a sub-frame mounted IRS assembly, Nissan R230...
  20. T

    Differential Equations in simple mechanics?

    I came across a few problems in the Kleppner and Kolenkow book in which you must find the force of tension at specific lengths on a rope of mass m. They said you must use differential equations to solve these types of problems. How can you solve and use differential equations like this to get...
  21. W

    Differential cross-section for partonic collisions

    I am trying to calculate differential cross-section for partonic collisions (QCD) like q + q \rightarrow q +q q + \bar{q}\rightarrow q + q g + g \rightarrow g + g I can't find those calculations done anywhere, just the results and maybe some middle tips, that's all. As you may know those...
  22. B

    Differential equations and escape velocities

    Homework Statement Good day all! I'm stumped on a question: If I fire a bullet straight up what will be the initial velocity such that the bullet doesn't come back down? I need to model a differential equation (it will be first order) some how! Also, Gravity is not constant, but rather, the...
  23. A

    Applied Differential Equations in physics

    Hi everyone, First of all, this is an awesome place :) I'm looking for a differential equation book, with partial differential equation (and Fourier series solution) that really goes into physics. I'm a 3-year undergrad student in Physics so I already know a little about it. By the way, for now...
  24. M

    Unsteady state heat transfer differential equation

    I'm going through the solution to a problem that was assigned to my class and there's a step I don't really understand which I think is a concept I'm misunderstanding. 1. Homework Statement The curved surface of a cylinder of radius R and length L is insulated. The face at x = L is maintained...
  25. M

    Other Looking for a good differential equations text

    Good afternoon, I've been working my way through Serge Lang's series of textbooks, and I recently completed A First Course in Calculus. I'm currently working through the sequel to that book, Multivariable Calculus, and that should keep me tied up for at least two months. Looking ahead...
  26. C

    Linearity in differential equations

    Homework Statement Is the equation (x2sinx + 4y) dx + x dy=0 linear This problem also asks me to solve it, but I don't have a problem with that part. Homework Equations An equation is linear if the function or its derivative are only raised to the first power and not multiplied by each other...
  27. D

    Differential calculus, physics problem

    Homework Statement The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber in a car) is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion of a point on such a spring is s(t) =...
  28. B

    Help Differential Equations types

    Homework Statement Good day all, My professor gave my class a packet of about 40 differential equations. I for the life of me cannot figure out how t solve these last 4! I also have an exam tomorrow morning, and would like finish these last few. I don't need them solved out, I would just...
  29. T

    Understanding Differential Equations: Exploring Relations between Functions

    Hello, I have a question that is relevant to differential equations. Say for example I have two functions that are related to one anothers derivatives. For example, the voltage acrossed an inductor is proportional to the rate of change of current through that inductor. My question for you is...
  30. O

    How to reduce higher order partial differential equations

    Hello guys, I have the system of PDE below and I want to solve it using finite difference method but I think I have to reduce it first to a system of first order PDE. The problem is that I don't know how to reduce this PDE to a first order system. I will appreciate any hints in this regard...
  31. L

    Nonlinear Ordinary Differential Equation Help

    Homework Statement y'=(x^2 +xy-y)/((x^2(y)) -2x^2)[/B]Homework EquationsThe Attempt at a Solution I know that really the only way to solve this one is to use an integrating factor, and make it into an exact equation. My DE teacher said that to make it into a exact equation you need to take...
  32. S

    MHB Second-order homogeneous linear differential equation

    Consider the second-order homogeneous linear differential equation $y'' + 4y' + Ky = 0$ Find the general solution if $K = 4$ So here is what I have: $r^2 + 4r + 4 = 0 $ =$(r + 2)(r+2)$ $r=-2$ ? But I thought that you can't do this because you won't be learning anything new if you have two of...
  33. stevendaryl

    How Do Spinors Fit in With Differential Geometry

    When I studied General Relativity using Misner, Thorne and Wheeler's "Gravitation", it was eye-opening to me to learn the geometric meanings of vectors, tensors, etc. The way such objects were taught in introductory physics classes were heavily dependent on coordinates: "A vector is a collection...
  34. PWiz

    Where do I start learning differential geometry?

    I've recently finished tackling differential equations. I want to start learning general relativity, but from what I've read, I need to have a firm footing in differential geometry first. So where do I start learning DG? I really don't want to do a half-hearted job in an attempt to quickly jump...
  35. evinda

    MHB Solution of differential equation

    Hello! (Wave) I am looking at the following exercise: We consider the differential equation $x^2y'+2xy+1=0$, where $0<x< +\infty$. Show that each solutions goes to $0$ while $x \to +\infty$. Find the solution $\phi$ of the above differential equation so that $\phi(2)=2 \phi(1)$. That's...
  36. resurgance2001

    Solving Simple Differential Equations: Particle Velocity and Position

    Homework Statement Given that a particle has an initial velocity v0 and then undergoes an acceleration a = - bv. , where b is a constant, obtain an expression for v = v(t) and x = x (t) [/B]Homework Equations Not sure The Attempt at a Solution If I integrate a = - b v I think I get v +...
  37. Dethrone

    MHB Differential Equation Challenge

    Find $y(x)$ to satisfy $$ y(x)=y'(x)+\int e^{2x}y(x) \, dx+\lim_{{x}\to{-\infty}}y(x)$$ given $$\lim_{{x}\to{0}}y(x)=0$$ and $$\lim_{{x}\to{\ln\left({\pi/2}\right)}}y(x)=1.$$
  38. L

    Second order differential equation

    Homework Statement So I'm in pchem right now and I haven't taken dif eq (it's not required, but I wish I had taken it now!) I am asked to solve this differential equation: y''+y'-2y=0 Homework Equations I know for a second order differential equation I can solve for the roots first. If...
  39. Logan Land

    MHB Need help setting up Differential Equation to solve

    dy/dx = (2y-x+5)/(2x-y-4) y(1)=1
  40. B

    Calculating Differential Mode Gain - CMRR, Acm, Adm

    Homework Statement http://i59.tinypic.com/1smqlu.png I'm not sure how to calculate differential mode gain Homework Equations I know formuals for CMRR and Acm but not Adm CMRR = | Adm/Acm | Rb/Ra = (1-ε)Rd/Rc
  41. hideelo

    Relationship between thermodynamics and differential geometry

    I am taking thermodynamics this semester as well as a course in differential geometry of surfaces, and I am seeing a lot of overlap. For example, I can create a "state space" isomorphic to R3 of TxPxV I can then define a surface on this space of PV=NkT I can define quasi static state equations...
  42. G

    Solution to differential equation

    Homework Statement This is actually a problem from my physics textbook, but I think it's mostly a mathematical problem, which is why I post it here: Show that the Langevin equation 1: \frac{dv}{dt}=-\gamma v+\frac{1}{m} F'(t) is solved by 2...
  43. C

    Curved-space Maxwell equations by differential forms?

    The flat-space source-free Maxwell equations can be written in terms of differential forms as $$d F = 0; \ \ d \star F = 0.$$ And in the theory of gauge fields, one can introduce a connection one-from A from which one can formulate general Maxwell equations (for Yang-Mills fields) by $$ dF + A...
  44. samjohnny

    Solving for v: Seeking Guidance for Differential Equation

    Homework Statement Kindly see the attachment. Homework Equations The Attempt at a Solution As with all such questions, its in setting everything up that I'm having some trouble. I know that F = mdv/dt + vdm/dt. And also that F = R - m(t)g, but R = M0g. From here though I don't know how to...
  45. W

    Need help solving second-order nonlinear differential eq

    Hello, I'm a doctoral student in civil engineering. In my research I came across a differential equation for the net force acting on an object as it impacts a granular medium at low velocities. z'' + a[ z' ]^2 + b[ z ] = c Where a, b, and c are all constants I believe that this equation will...
  46. B

    Can you cancel a function out of a differential equation?

    I saw this in http://en.wikipedia.org/wiki/Momentum_operator From equation 4 to 5, it seems that a function is canceled out from the partial derivatives, is this possible?
  47. M

    Solving a differential equation

    Homework Statement Solve (xy+y2+x2) dx -( x2 )dy = 0 Homework Equations to verify if exact http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngM/[PLAIN]http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngy =...
  48. L

    Homogenous and linear differential equations

    Homework Statement I am currently in quantum chemistry, and in class one day my professor spent some time talking about Maxwell's equations. I am looking at my notes, trying to piece together Maxwell's equations, differential equations, and the principle of superposition, since this is not in...
  49. KD1729

    MHB Identifying the Degree of a Differential Equation

    How Can we define the degree of differential equation ? What is the degree of $$\left(\frac{{d}^{2}y}{d{x}^{2}}\right)^{\!{2}}\left(\frac{dy}{dx}\right)^{\!{3}} +\left(\frac{dy}{dx}\right)^{\!{1}} =0$$ ??(Wondering)
  50. T

    Any value to Spivak's Differential Geometry set?

    I have the hardback 5 volume set of Spivak's A Comprehensive Introduction to Differential Geometry that is in pretty good shape. Is there any value to that set? I tried looking it up, but I don't really see many people selling whole sets, so I can't tell... Thanks.
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