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A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics and other disciplines. Visualization of airflow into a duct modelled using the Navier-Stokes equations, a set of partial differential equations.Differential equations arise in many areas of science and technology; whenever a deterministic relationship involving some continuously changing quantities (modeled by functions) and their rates of change (expressed as derivatives) is known or postulated. This is well illustrated by classical mechanics, where the motion of a body is described by its position and velocity as the time varies. Newton's Laws allow one to relate the position, velocity, acceleration and various forces acting on the body and state this relation as a differential equation for the unknown position of the body as a function of time. In many cases, this differential equation may be solved explicitly, yielding the law of motion. An example of modeling a real world problem using differential equations is determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance. Gravity is constant but air resistance is proportional to the ball's velocity. This means the ball's acceleration, which is the derivative of its velocity, depends on the velocity. Finding the velocity as a function of time requires solving a differential equation. Differential equations are mathematically studied from several different perspectives, mostly concerned with their solutions, functions that make the equation hold true. Only the simplest differential equations admit solutions given by explicit formulas. Many properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy. From Wikipedia under the
GNU Free Documentation License  mathhelpforum.com razemsoft21 Sat, 27 Jun 2009 20:21:07 GM any 1 can help me on solving the following question plz. Use Frobenius method to solve the following . differential equation. X2Y'' +X(2-X)Y'-2Y= 0.  marcofrasca.wordpress.com mfrasca Sun, 28 Jun 2009 11:04:06 GM A typical application is exactly in the area of . differential equations. where you can have some varying parameters. But the possibilities are huge for this method and, indeed, you can find almost 5000 demonstrations at that site. ...  mastiabhilash.blogspot.com abhilash Sat, 13 Jun 2009 14:44:00 GM Differential equations. : First order . equation. (linear and nonlinear), Higher order linear . differential equations. with constant coefficients, Method of variation of parameters, Cauchy's and Euler's . equations. , Initial and boundary value ... From Google Blog Search: "differential equations"  news.google.com Satellite Today (subscription) Ability to work with mathematical concepts such as probability, statistical inference, calculus, differential equations , and fundamentals of plane/solid ... news.google.com ScienceBlogs If we've got a system that's described using differential equations , we might be able to integrate them analytically, and figure out what f is; ... news.google.com Groundviews I can simulate stochastic differential equations and find uncertainties in their solutions . Ever read anything broader than that? he mocks. ... From Google News Search: "differential equations" What exactly are differential equations? Q. I 'think' I know what they are but I'm not sure...for example most problems I see are in the format y prime = y or somthing like that. To me it seems to find a 'solution' y for the differential eq you would have to find a function y...that is also...its own derivative. The only thing I can think of is e^x. Is this kinda what diff eqs are all about? What if there was a question... y prime = y and y = x^2 ...how do you solve something like this?? How do you solve for y in diff eq's in general?? And how exactly do they predict somthing? Please use an example if possible. One last thing: sometimes they ask "what can you say about a solution of the diff equation just by looking at it?" -what are some strategies to use to know how… [cont.] Asked by adro701 - Sat Aug 11 22:03:25 2007 - - 4 Answers - 0 Comments A. A differential equation is any equation that has a differential in it, be it y prime, y double prime or whatever. When you find a solution, you do find what y is. y prime = y and y = x^2 has no solution, since y prime = 2x, which isn't y. So you can't solve that one. I don't know what you mean for predicting something or the "just by looking at it" thing though, sorry. And the point (2,4) is not a solution to a differential equation. You can't take the derivative of (2,4), and you can't generally divide by x either because the function y = x^2 includes x=0. Answered by mj - Sat Aug 11 22:37:12 2007 Is it possible to find a continuous function h(y) such that the one-parameter family of differential equations? Q. dy/dt=h(y)+ satisfies the following statements? For all -3, the differential equation has exactly two equilibrium points the smaller one is a sink and the larger one is a source. For all 3, the differential equation has no equilibrium points. For =0, the differential equation has exactly four equilibrium points. Asked by Bobby M - Thu Sep 4 18:26:39 2008 - - 1 Answers - 0 Comments A. To me, this sounds the same as asking whether there is a continuous function h(x) such that: 1) y = h(x) - 3 descends across the x axis, wiggles a bit, and then ascends across the x-axis. 2) y = h(x) + 3 has no real roots. 3) y = h(x) has exactly four real roots. Since the function h(x) = (x-2)(x-1)(x+1)(x+2) meets these conditions, I suppose the function h(y) = (y-2)(y-1)(y+1)(y+2) will work for you. Answered by Doc B - Sat Sep 6 02:42:09 2008 I need to solve a system of partial differential equations and I am struggling with it for days?
Q. I would really like a useful resource or any kind of help because I am getting really desperate and I need to solve these equations because my grade depends on them If you are clueless then dont try to be funny cuz you are not Asked by aurora442x - Wed Jan 9 22:14:38 2008 - - 7 Answers - 0 Comments A. Check out OpenCourseware on the MIT website. It might have a PDE class on there. If you're in college, you should have access to Matlab somewhere on campus. You could also use a TI-89 or 92 if you can turn each PDE into a system of ODEs, and then solve the larger system. Answered by Drew F - Wed Jan 9 22:32:24 2008 From Yahoo Answer Search: "differential equations" |
