What is First order: Definition and 585 Discussions

In mathematics and other formal sciences, first-order or first order most often means either:

"linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of higher degree", or
"without self-reference", as in first-order logic and other logic uses, where it is contrasted with "allowing some self-reference" (higher-order logic)In detail, it may refer to:

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  1. S

    First Order DE Problem: Self-Teaching Derivatives

    I've been kind of self teaching myself first order derivities... this is really my first shot at it.. want to know if this is right so far \frac{dy}{dx} = \frac{y(1-x^5y)}{x} xdx = y (1-x^5y)dx xdy = (1y-x^5y^2)dx xdy = ydx - x^5y^2dx \frac {xdy - ydx}{y^2} = \wr -x^5dx \wr d\frac{x}{y} =...
  2. R

    First order differentials: separating variables

    "Find the general solution to the differential equation by separating variables: 3tany - dy/dx(secx) = 0" This is what I set up: 3tany dx = secx dy 1/secx dx = 1/3tany dy cosx dx = 1/3tany dy [int] cosx dx = [int] 1/3tany dy sinx = (1/3)ln|sinx| I'm stuck as to what to do next...
  3. R

    First order differentials & euler's method

    I'm having trouble solving first order differential equations for euler's method. right now I'm trying to figure out: y' = x + y y(0) = 1 i have: dy/dx - y = x p(x)=-1 , q(x)=x u=e^(-x) y=e^x [integral](xe^-x)dx .. i don't think I'm doing this right, where am i going...
  4. D

    Solve homogeneous first order PDE's

    u_x+u_y+u=e^{x+2y}, y(x,0)=0 I have no idea how to do this. We were only taught how to solve homogeneous first order PDE's.
  5. H

    Asymptotic mathcing for a first order differential equation

    The first-order differential equation y' +(ex^2+1+1/x^2)y=0, with boudary value y(1) =1 Using, asymptotic mathcing to study the behaviour of the sltion as e tends to +0, when x is not too large, the term ex^2 is negligible so an approximate equation for y is y'_L +(1+1/x^2)y_L=0 . When...
  6. H

    Asymptotic mathcing for a first order differential equation

    The first-order differential equation y' +(ex^2+1+1/x^2)y=0, with boudary value y(1) =1 Using, asymptotic mathcing to study the behaviour of the sltion as e tends to +0, when x is not too large, the term ex^2 is negligible so an approximate equation for y is y'_L +(1+1/x^2)y_L=0 . When...
  7. N

    Proving the Solution to a First Order Linear Differential Equation

    Hello all, I'm trying to prove to myself that the following solution to the DE shown works. I can't start using it until i prove to my self it works (it's this psycological thing i have were i can't use anything unless i know where it comes from). :smile: Here is the Equation and it's...
  8. S

    Solving First Order Differential Equations - A Beginner's Guide

    I am new to to this topic, hints? y^1=x+5y The only examples are in the form dy/dx+p[x(y)]=Q[x]
  9. M

    Differential Equation first order help

    Can anybody tell me what can be the solution of this differential equation? (dr/dt)^2=a/r^2+b/r+c Is first order and i need some ideas about solving it
  10. C

    Degree of first order coherence and fluctuations

    Hi! I'm new here, but I hope that someone would evenly help me! My first question is about the problem (3.3 on page 100 from Loudon - The Quantum Theory of Light 3ed) in the attachment; the second question is about discussing (I)the physical origin of fluctuations of the electromagnetic...
  11. M

    How Can I Solve a Unique First-Order ODE Numerically?

    I would like to solve a problem of the type (da/dt)^2 + f(a)* (da/dt) = g(a) (1) a=a(t) unknown function f(a), g(a) = known functions of a. This differential equation is a first order ODE but (da/dt)^2 makes it different compared to a typical first order ODEs (at least to my...
  12. J

    Nonlinear First Order Differential Equations

    Hello. I am taking a self study diff e course, and I have run into a problem with no one to ask for help. Here is the problem: y\prime=1+x+y^2+xy^2 The question asks to find the general solution. I simply don't understand how to solve this problem. Here is the direction I am going in...
  13. M

    How Can This Non-Separable First Order ODE Be Solved?

    Does anyone see how one can tackle the following ODE? [2y*exp^{y/x} + x}] \frac {dy} {dx} -2x - 2y = 0 that is my attempt: rearrange to get dy/dx = \frac {2x + 2y} {2y*exp^{y/x}-x} I do not see how to go on from here. Surely, the ODE is not seperabale and I don't find a way...
  14. X

    First order differential equation help

    i've derived the following differential eqn from a problem I'm working on, and i have tried in vain to solve this if anyone can give a direction where i should go our how to attack would be greatly appreciated. the eqn is I\,r= -L\dot{I}+\frac{3}{2}\mu_{0}m R^{2}\frac{z...
  15. M

    Confused on a first order seperable diff EQ wee

    Hello everyone. I'm going back to all my old webworks and trying to finish them and I'm still having problems on first order. It says this is seperable but I'm not seeing it. Here are the directions: The differential equation...
  16. S

    Solution of a first order ODE.

    We have the first order ODE y'=4t \sqrt y,~y(0)=1, for which i have found the exact solution, namely a fourth order polynomial. I want a numerical method to solve the problem exactly. This method has to be a fourth order method, since this implies that the local error vanishes. Now...
  17. M

    First order differential equation

    Just need a hand with this one. (dy/dx)x + 2y = x^3.ln(x) (dy/dx) = (x^3.ln(x) - 2y)/x Integrating factor = x^2 (dy/dx)x^2 + 2xy = (x^3.ln(x))x^2 yx^2 = INT[(x^3.ln(x))x^2] I'm having trouble integrating the last part to complete it. Thanks a lot and in advance for any help.
  18. D

    Solving Nonlinear First Order Differential Equations | Methods and Techniques

    Hi, As far as I know this is a first order, nonlinear diff eqn with both dependant and independant variables...so it is not solvable?? y'+ay^2 = bx If anybody knows if there is a method to solving it, please let me know. Thanks, danmag :confused:
  19. S

    Answer: First Order Reaction Rate Constant at 593K

    The first-order reaction, SO2Cl2 --> SO2 + Cl2, has a rate constant equal to 2.20 x 10-5 s-1 at 593 K. What percentage of the initial amount SO2Cl2 will remain after 2.00 hours? a.1.00% b.14.7% c.17.1% d.85.4% ln [a]t/[a]0 = -kt ln [a] = -(2.20 x 10-5...
  20. Z

    Integrating Factor Method for Solving Linear First Order Equations

    I'm using an integrating factor, rho(x), to solve an equation of the form dy/dx + P(x)y = Q(x) I need to find the particular solution. y' = 1 + x + y + xy; y(0) = 0 y' - y - xy = 1 + x dy/dx + y(-1-x) = 1 + x P(x) = (-1-x), Q(x) = (1 + x), rho(x) = e^(-x-1/2x^2) (Multiply both sides by rho(x))...
  21. A

    First order logic: Soundness, Completeness, Decidability

    So I'm a bit confused about these metatheorems about first order logic, partly because I haven't read any of the real proofs, but I just want to know the results for right now. Here is what I understand: Soundness means that any derivation from the axioms and inference rules is still valid...
  22. G

    Solving a first order differential

    I have the following problem that i can't get the right answer to: y'+y=5sin(2t) I find the integrating factor u(t)=e^t multiply the whole function u(t) and i get (ye^t)'=5e^tsin(2t) I do integraton by parts on the second part and get 1/9 for the coefficents, in the calculator they...
  23. M

    [DiffEq] First order Modeling Applications

    YATP - Yet Another Trainlike Problem Sailboats A and B each have mass 60kg and cross the starting line at the same time of a race. Each has an initial velocity of 2m/s. Obviously from this, m1 = m2 == 60kg and vo1 = v02 == 2 m/s. The wind applies a constant force of 650N to each boat and...
  24. L

    Solving 1st Order ODE: f(s) = -F(s)ln(s^2 + 1)/2 + C

    I need to solve the following for f(s): (s^2 + 1)f '(s) + s f(s) = 0 First I isolated for f '(s), which gave me: f '(s) = -s f(s)/(s^2 + 1) Then, d f(s)/ds = -s f(s)/(s^2 + 1) so, d f(s) = (-s f(s)/(s^2 + 1))ds Integrating I get: f(s) = -F(s)ln(s^2 + 1)/2 + C, where F(s)...
  25. K

    First order coupled differential equations

    Hello I'm struggling with this concept, can't seem to get my head round it or find any good reference sites or books. I have calculated the eigen values and eigen vectors for the following matrix 5 3 1 7 Eigen values 4, 8 Eigen vectors 4: 3 -1 Eigen...
  26. R

    Coupled first order differential equations

    How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.
  27. R

    Coupled first order differential equations

    How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.
  28. D

    Linear first order differential equations - just a question

    I thought the general solution of the linear first order differential equation y ^{\prime} + p(t)y = g(t), \qquad y\left( t_0 \right) = y_0 were y = \frac{1}{\mu (t)} \left[ \int \mu (s) g(s) \: ds + \mathrm{C} \right], where \mu (t) = \exp \int p(s) \: ds However, I have found...
  29. D

    First Order Differential Equation

    "A recent college graduate borrows $100,000 at an interest rate of 9% to purchase a condominium. Anticipating steady salary increases, the buyer expects to make payments at a monthly rate of 800(1 + t/120), where t is the number of months since the loan was made. Assuming that this payment...
  30. Oxymoron

    Verify Solutions to First Order PDEs

    Just need some verification. Question 1 Find the general solutions of the following first order PDE z_x - yz_y = z Question 2 Find the general solution of the following first order PDE x^2z_x+y^2z_y = xy
  31. S

    Solving Linear First Order D.E. y' - y*tan[x] = 2sin[x]

    Solve y’ – y*tan[x] = 2sin[x]. I keep arriving at the answer: y = 2ln(sec[x]) / sec[x] - c/sec[x] for this question. According to my textbook the correct answer is: y = (c - cos[x]) * sec[x]. Can anyone explain how to obtain this answer? Thanks :)
  32. G

    Tableau Proof for All x P(x) V Q(x) $\supset$ Exists y P(y) V Exists z Q(z)

    To do a tableau proof of this statement: (\forall x) [P(x) \vee Q(x)] \supset [(\exists x)(P(x) \vee (\exists x)(Q(x)] I started out by restating it as follows: (\forall x) [P(x) \vee Q(x)] \supset [(\exists y)(P(y) \vee (\exists z)(Q(z)] to avoid confusion over what's bound to what (and...
  33. M

    What Methods Can Be Used to Solve Coupled First Order PDEs?

    I am looking for a method to solve coupled first order PDEs in following form: \frac {\partial u1} {\partial x} = f(x,t,u1,u2) \frac {\partial u2} {\partial t} = g(x,t,u1,u2) Subject to prober BC and IC. and consider: u1=F(x,t) u2=G(x,t) I am looking for...
  34. W

    First Order Linear Differential Equations

    Hello, It has been over a year since I last did calculus. And I am having trouble with my current calculus course. First here is the question: Solve the given first-order linear equation and verify that your solution indeed satisfies the equation. y' - 2xy = 2xe^x^2 Now I THINK I...
  35. quantumdude

    Propositional and First Order Logic

    Is total formalization possible? If not, why not? The following is a first course in formal mathematical logic. http://www.trentu.ca/academic/math/sb/pcml/pcml-i-15.pdf Looking through the book, I do not see any that the author presupposes any mathematical knowledge. Volume II...
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