# Differential Equations

- An equation involving derivatives of a function or functions. Solving ODE and PDE
 Meta Thread / Thread Starter Last Post Replies Views Views: 124,632 Announcement: Follow us on social media and spread the word about PF! Jan16-12 Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 09:24 AM micromass 1 29,630 Pinned: Intro. to Differential Equations ( 1 2 3 ... Last) My intent is to create a thread for people interested in Differential Equations. However, I will explicitly state that... Jul3-12 07:18 PM Luccas 95 136,780 I know that the standard definition for a slope field is ##\frac{dy}{dx} = f(x, y)##, but and if the equation given is... Apr13-14 04:08 PM HallsofIvy 1 256 f(x,y) = ln(9 - x2 - y2) Domain I got: (x, y) in R2 such that x2 + y2 < 9 How do I find the range from the... Apr12-14 12:09 PM JC3187 6 336 Show that the explicit Runge-Kutta scheme $$\frac {y_{n+1} -y_{n}}{h}= \frac{1}{2}$$... Apr10-14 07:21 PM rickyflair 2 323 If a system of first-order ODEs like ##\frac{d\vec{r}}{dt}=A\vec{r}## have as solution ##\vec{r} = C_1 \exp(\lambda_1... Apr10-14 02:58 PM Jhenrique 9 527 Hi All, I am taking Dynamic Systems and Controls this semester for Mechanical Engineering. We are solving non... Apr9-14 12:40 AM MisterX 1 365 You can give me a good examples where ##\frac{\partial}{\partial x}## is different to ##\frac{d}{dx}## ? Apr8-14 09:12 AM Jhenrique 2 358 Hello I am having some trouble understanding what the difference is between the reference solution and the "true"... Apr7-14 07:36 AM jjr 2 423 Hello guys, suppose we have an eigenvalue problem \left\{ \begin{array}{ll} u'' + λu = 0, ... Apr2-14 10:44 AM AlephZero 6 499 I realized that a PDE of 2nd order can written like: A:Hf+\vec{b}\cdot\vec{\nabla}f+cf=0 \begin{bmatrix} a_{11} &... Apr1-14 09:22 PM Jhenrique 0 324 Hi, I am looking for a solution of \frac{\partial\phi}{\partial t} =... Apr1-14 06:50 AM soni 0 317 Which the difference between diff equations of kind: \frac{dy}{dx} = \exp(x) \frac{dy}{dx} = 1/x and diff equations... Apr1-14 02:22 AM Mark44 8 383 Hello, I have been trying to find an equation to represent the observed angular velocity of any object traveling in a... Mar31-14 08:50 PM bendloewen 3 403 Hello, I'm trying to analyze a system of elastically coupled oscillators, whose masses are all the same, using... Mar31-14 10:51 AM Runei 1 293 Hello, I am doing some physics and I end up with this PDE: \frac{\partial q(x,y,t)}{\partial t} = -(x^2 +... Mar28-14 02:51 PM kosovtsov 4 678 How do we solve a system of coupled differential equations written below? -\frac{d^2}{dr^2}\left( \begin{array}{c}... Mar27-14 11:04 PM Ravi Mohan 2 450 Given a implicit ODE like F(x, y(x), y'(x), y''(x)) = 0, why your explicit form is y''(x) = f(x, y(x), y'(x))? Why a... Mar27-14 12:36 PM micromass 4 408 If we have a constant coefficient second order homogeneous ODE, the way to solve this is to suppose a solution of the... Mar27-14 08:13 AM quasar987 4 368 hello pf! i am wondering if anyone here knows of a geometric, intuitive explanation for the laplace transform? if... Mar26-14 05:34 PM micromass 3 350 I would like to learn this. Can someone teach me? The things like δy2/δ2x and solving for x and y. :rolleyes: Mar26-14 12:37 AM z.js 10 664 I want to solve y''+y'+y=(sin(x))^2 and try to use y=Ae^{ix} but then when I square it I get A^2 e^{2ix} ... Mar26-14 12:26 AM lurflurf 1 317 Hi, I know the weak form of the Poisson problem \nabla^2 \phi = -f looks like \int \nabla \phi \cdot... Mar25-14 01:12 PM pasmith 1 369 It is very clear that the solution to the equation "dy/y-a*dx/x = 0" is y=C*x^a. However I cannot figure out the... Mar24-14 05:27 PM maajdl 5 337 Apparently it is a well-known fact that if G(x)=(G_{ij}(x_1,\ldots,x_n)) is a smooth nxn matrix-valued function such... Mar20-14 03:04 PM quasar987 0 464 px = t t = s^2 $$I = \int_0^∞ e^{-s^2}ds$$ I*I = \int_0^∞ e^{-s^2}ds * \int_0^∞ e^{-u^2}du = \int_0^∞\int_0^∞... Mar19-14 03:11 PM HallsofIvy 2 457 Hi, this question came up in my midterm and I was hoping to know if this is the correct method or answer. Mar18-14 04:18 PM pasmith 5 502 Hello, I am learning about the general solution to higher order linear non-homogeneous differential equations. I know... Mar17-14 11:59 PM lurflurf 1 391 I am trying to work though an example on this topic in my book and have reached a point that I am not sure about. I... Mar17-14 04:00 PM jellicorse 2 341 I've been playing around with the following system for the last little while: (attached image: 2 Blocks +... Mar17-14 07:35 AM aragorn77777 2 421 Hi there, I am trying to solve a structural mechanics problem. I am doing so by two methods. On one hand, I am... Mar16-14 07:33 PM c.teixeira 0 337 Hi, I have been experimenting with FreeFem++, and have alos found a list of other free finite element packages. ... Mar16-14 10:09 AM Morberticus 0 318 Hi everyone, I have a question on the rate constant of a kinetic model(like the one we use in describing chemical... Mar13-14 07:50 PM Chestermiller 3 408 How do you decide on the sign of a Hamiltonian function? For example, I have the following system of differential... Mar13-14 09:21 AM luitzen 0 340 Hi, it is easy solving these PDEs with the idealized homogeneous BCs they throw out in class, but I am having some... Mar12-14 08:49 PM Chestermiller 9 675 Hello! My goal here is to plot the solution to the bioheat equation for a tumor as a function of time. I'm plotting... Mar12-14 04:08 PM Chestermiller 9 498 Hello, As of recently, I've been working with Laplace transforms and have a question about their relationship to... Mar11-14 09:58 AM the_wolfman 6 733 Hello, does anyone knows the Integral of (dx)^2 Excuse my english, I hope I had make myself clear, thanks Mar8-14 07:08 PM micromass 6 563 I was wondering if somebody could clear up some confusion I have regarding this. I've been going over the... Mar8-14 06:56 AM jellicorse 2 337 Hello,Iam facing a problem with using FindMinimum Function .Can any body help me ? First I used FindRoot fuction to... Mar8-14 03:45 AM Reem Hashem 0 282 Notice that, when solving second-order linear homogeneous constant-coefficient ODEs, the classic linearly independent... Mar6-14 02:18 PM lurflurf 1 400 By a fortuitous mistake in copy/pasting, I happened across this system. It exhibits very chaotic behavior for some... Mar6-14 08:40 AM TylerH 1 356