First order Definition and 585 Threads

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. W

    First order integro differential equation

    Can anyone help me to solve a differential equation? I want to solve ∂v(p,t)/∂t=-p^2 v(p,t)-sqrt(2/pi)∫v(p,t)[1-δ(t)R(t)]dp+sqrt(2/pi)[δ(t)R^2(t) C] with initial data v(p,0)=0 where C is constant and the integration from zero to infinty Any suggestion please? Solution by volterra integral...
  2. D

    What does " to first order" mean ?

    Hi. When using approximations such as g = n + h where h is much less than n ; what does " valid to first order in h" mean ? Does it mean include terms linear in h or does it mean drop those terms ? Thanks
  3. L

    First order differential equations and constants

    Homework Statement ##y' = \frac{cos x}{sin y}## ##y' = \frac{6x^2}{y(1 + x^3)}## Homework EquationsThe Attempt at a Solution So I was working through some textbook problems and there's something about the solutions of the above equations I don't quite understand. The first one: ##\int sin...
  4. AAO

    First Order D.E (Not Linear, Exact, or Separable)

    Homework Statement What is the general solution of: y'=(3*y^2-x^2)/(2*x-y) Homework EquationsThe Attempt at a Solution This First Order equation is neither linear nor separable. I also have checked the Exact test, which turns to be Not Exact. Any help regarding how...
  5. W

    Solving First Order Linear ODE: dy/dx = y/x + tan(y/x)

    Homework Statement Solve dy/dx = y/x + tan(y/x) Homework EquationsThe Attempt at a Solution Not separable, as far as I can tell. It's not homogeneous, since for the tan term f(λx,λy) = tan(λy/λx) = tan(y/x) ≠ λtan(y/x). It's also not of the form dy/dx + P(x)y = Q(x), because I don't think Q(x)...
  6. MTd2

    New first order Lagrangian for General Relativity

    http://arxiv.org/abs/1503.08640 New first order Lagrangian for General Relativity Yannick Herfray, Kirill Krasnov (Submitted on 30 Mar 2015) We describe a new BF-type first-order in derivatives Lagrangian for General Relativity. The Lagrangian depends on a connection field as well as a...
  7. Prof. 27

    First Order Linear Differential Equation

    Homework Statement dv/dt = 9.8 - 0.196v Set in correct form: dv/dt + 0.196v = 9.8 Since p(t) = 0.196, u(t) the integration factor is given by: u(t) = e∫0.196 dt Multiply each term by u(t) and rearrange: (e∫0.196 dt)(dv/dt) + (0.196)(e∫0.196 dt)(v) = (9.8)(e∫0.196 dt) From now on we will set...
  8. binbagsss

    System of first order equations, matrix form, quick question

    Question: ##h_{t}+vh_{x}+v_{x}h=0## ##v_{t}+gh_{x}+vv_{x}=0## Write it in the form ##P_{t}+Q_{x}=0##, where ##P=(h,hv)^{T}##, where ##g## is a constant ##>0##, and ##v## and ##h## are functions of ##x## and ##t##. Attempt: I have ##Q=(vh,?)^{T}##, the first equation looks easy enough, but...
  9. Marcis Rancans

    Why Does a Constant Appear Only on One Side in This Differential Equation?

    I don't understand this first order differential equation: https://lh5.googleusercontent.com/UUpQF4YjmjJRPvFuzGg2MhpMMMDyi2KFZPCKMKVIXGREc1owvXDzGR0bcA=s600 How is it possible to get an exponent as answer?
  10. I

    First order RC: Find Unknown DC Circuit, given current graph

    Homework Statement Homework Equations [/B] Tao = R(th) C The Attempt at a Solution The unknown DC circuit model consists of a V(th) and R(th) Tao = (R(th) + 3000) C , total resistance of circuit is R(th) + 3000 0.004 = (R(th) + 3000) (1x10^-6) R(th) = 1 kOhm The V(th) should oppose the...
  11. A

    Diffraction grating with high intensity in first order

    I'm searching for a reflexive diffraction grating with at least 1500 line per mm and high intensity in first order. Common reflexive diffraction grating don't have enough intensity for my experiment. I need to help for getting such grating. Thanks
  12. S

    Substitution to convert first order ODE to homogenous

    Homework Statement Use the substitution ##x=X+h## and ##y=Y+k## to transform the equation ##\frac{dy}{dx}=\frac{2x+y-3}{x-2y+1}## to the homogenous equation ##\frac{dY}{dX}=\frac{2X+Y}{X-2Y}## Find h and k and then solve the given equation Homework EquationsThe Attempt at a Solution If I...
  13. X

    How Does K1 Being Zero Affect the First Order Circuit Solution?

    Homework Statement We are given K1 = 0. So the answer should be in the form of V(x) = K2e^(-t/z)Homework Equations V=IR V(x) = K1 + K2e^(-t/z) V(infinity) = K1 V(0+) = K1 + K2 z = RC The Attempt at a Solution I draw the circuit for t = 0- and find the voltage across the capacitor. Vc(0-)...
  14. U

    Convert sentences into First Order Logic

    (1) Anyone who is thin, tall and energetic will be good basketball player. (2) Some people are tall but not good basketball players. (3) Anyone who do exercise or eating healthy food will be energetic. (4) Saman is thin and tall person who do exercises. Write the above sentences in First Order...
  15. MexChemE

    Integrating factor vs. Laplace. Engineering problems

    Hello PF! We were doing mass balances on mixing tanks in one of my ChemE courses, and in one of the problems we arrived at the following DE: \frac{dC_B}{d \theta} + 0.025C_B=0.0125 e^{-0.025 \theta} Where CB is the concetration of salt in the tank and θ is time. The professor made us solve the...
  16. 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...
  17. M

    Solving Non-linear First Order ODEs with Variable Coefficients?

    Homework Statement $$y' y + \frac{y}{x} = 1 - 2x$$ Homework Equations nothing comes to mind The Attempt at a Solution i've guessed a quadratic but that didn't work. now I'm stuck. any ideas? also, this is not homework, but a problem I am working on. Thanks!
  18. D

    Help with first order second degree diff. eq.

    Hi, can anybody help me with this differential equation? (px-y)(py-x)=a^2*p, where p=y'. I tried to solve it by expliciting the two solutions for y as functions of p and x and then derive, in order to obtain two first order differential equations in p but these are impossible to solve. I also...
  19. P

    First order ODE, orthogonal trajectories

    1. The problem statement, all variables and given/known da ##\frac{x^{2}}{k^{2}} + \frac{y^{2}}{\frac{k^{4}}{4}} = 1## with k != 0 this can be simplified to ##x^{2} + 4y^{2} = k^{2}## Find dy/dx implicitly, then find the new dy/dx if you want orthogonal trajectories to the ellipse. Lastly solve...
  20. H

    Multidimensional first order linear PDE

    Hello, I have the following PDE : v_y \frac{\partial f}{\partial y} + \Omega_x(y)\left(v_z\frac{\partial f}{\partial v_y} - v_y\frac{\partial f}{\partial v_z}\right) + \Omega_z(y)\left(v_y\frac{\partial f}{\partial v_x} - v_x\frac{\partial f}{\partial v_y}\right) = 0 (which is the steady...
  21. P

    Solving 1st Order PDE: Finding L with Ax^2 Form

    How to find L if the form is: $$ (\frac{\partial L}{\partial x})^2 - (\frac{\partial L}{\partial y})^2 = -1$$ The author wrote, $$L = y + ax^2 + ..$$ but I didn't get how?
  22. G

    Help with Differential Equations (First order)

    Homework Statement Solve the given the two equations: xdy + ydx = ydy and (y^2 + 1)dx +(2xy + 1)dy = 0 Homework Equations N/A. The Attempt at a Solution For the first, I can see that solving this with respect to dy/dxmight be a bit tricky. However, if I solve it for dx/dy, things...
  23. 2

    First order, linear PDE with unknown inhomogeneity function

    Homework Statement Solve the following IVP: ##\frac{\partial v(x,t)}{\partial x} + \frac{\partial v(x,t)}{\partial t} + v(x,t) = g(x,t)## Homework Equations The initial values: v(0,t) = a(t) and v(x,0) = b(x)The Attempt at a Solution I applied the Laplace transform x -> s to get...
  24. Z

    First order correction of wavefunction in degenerate perturbation

    In first order correction of wavefunction, |ψ(1)n>=∑ψ(0)m<ψ(0)m|V|ψ(0)n>/(E(0)n−E(0)m) when any two of the original states degenerate, we replace the two states with their corresponding "good states" to get a new set of "undisturbed" states (ψ(0)m), AND then we determine the first order...
  25. G

    Solutions to first order equation with Clifford algebra elements

    In the same way one can show that \nabla^{2}\theta=0 has only one smooth solution, namely \theta=0, I would like to show that \gamma^{i}\partial_{i}\epsilon=0 has only one smooth solution, where \gamma^{i} is a Dirac gamma matrix (or an element of the Clifford algebra), and \epsilon is a...
  26. C

    First Order ODE With v = y' Substitution

    Homework Statement 8t^2 * y'' + (y')^3 = 8ty' , t > 0 Homework EquationsThe Attempt at a Solution I tried using the substitution v = y' to get: 8t^2 * v' + v^3 = 8tv I rewrote it in the form 8t^2 * dv/dt + v^3 = 8tv, and then moved the v^3 to the other side to get 8t^2 * dv/dt = 8tv - v^3...
  27. S

    Calculating a matrix element & first order shift

    So I saw this a moment ago: How can the second and third terms yield (n+1)+(n-1)=2n and not (n+1)+n=2n+1? PS: I solved the problem by using [a,a(+)]=1. Sorry, this is very simple but I cannot figure out what I did wrong.
  28. D

    Differential equations - backwards problem

    Homework Statement If y=y(t) is the solution of the initial value problem { y'+(2t+1)y=2cos(t) y(0)=2 then y''(0)=? it is a multiple choice practice problem with choices y''(0)=2 y''(0)=-2 y''(0)=4 y''(0)=0 y''(0)=-4Homework EquationsThe Attempt at a Solution Im really not sure how to go...
  29. K

    Solving a First Order Initial Value Problem

    Homework Statement If y = y(t) is the solution of the initial value problem y' + (2 t + 1) y = 2 cos(t) y(0) = 2 What is y''(0)? Homework EquationsThe Attempt at a Solution Since this is a first order linear, I started out by finding the integrating factor so I can find what y is, and then...
  30. matt_crouch

    First order partial differential equation

    How do I go about solving a differential equation of the form \partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y) Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients...
  31. F

    MHB First Order Nonlinear Differential Equation

    Hi, I need help solving this ode, when I try to solve it I end up with a big crazy answer and I believe it should be simpler. (dy/dx)^2=((ay^4)/2)-(a+1)y^2+1 y(0)=0, y'(0)=1 and a is within [0,1]
  32. F

    MHB Solve 1st-Order ODE: Chicken in 375° Oven

    I'm going to need a little help with this one. I get an answer but it doesn't make sense. The question states According to Newton's law of cooling, the time rate of change of temperature T(t) of a body immersed in a medium of constant temperature A is proportional to the difference A-T. That...
  33. L

    Differential Equations Help, non-linear first order with substitution

    (r^2) (dT/dr)+B*r*T=T^2, with initial condition dT/dr |r=0 =0 where B is a constant I've gotten it to this: dT/dr = -BT/r + T2 / r2 by dividing everything by r2, then I substitute using λ= T/r which gives: r * dλ/dr + lambda = -B * (λ) + λ^2 I don't know how to separate...
  34. M

    First order minimum - Wave interference

    Hi :-) I'm currently learning about wave interference and came across two phrases I can't seem to find the meaning of; first order minimum and second order minimum. What do they mean an how are they used? I presume they are for the order of destructive interference or something?
  35. N

    MHB How Do You Calculate This Indefinite Integral in a First Order Linear ODE?

    Hi How do you calculate the following indefinite integral: \int \frac{2x}{125+3t} dt a step by step solution would be appreciated
  36. D

    Linear first order differential equation with unknown function

    I was wondering if there is a way to get specific numerical values for the following differential equation: f'(x)+ \frac{1}{x-20}\cdot f(x)=\frac{1}{x-20}\cdot g(x) I have numerical values for g(x) for about 10 different x values. I need to find f(x) numerically for those same values...
  37. S

    Yet another first order differential equation

    Homework Statement okey, so i got stuck at another step in the way of solving de's.I've been studying DE of this form: y' + P(x)y = Q(x) Homework Equations The Attempt at a Solution So, first we solve y' + P(x)y=0 for y. \frac{dy}{y} = -P(x)dx , we integrate this and get...
  38. S

    First order differential equation

    Homework Statement I'm starting college this autumn(physics) and I started learning some calculus on my own, basic stuff like first order differential equation and so on.Recently i stumbled on something that i don t understand.I was reading the course and re-solving the given examples for...
  39. gfd43tg

    Solving higher order ODE as system of first order

    For this problem, I am stuck on the actual system. I don't see what substitution I can make, and the fact that ##u(v)## is a piece-wise function is tripping me up. How the heck do I approach this?? This doesn't look like a standard problem at all.
  40. S

    Perturbation Theory - First Order Approximation

    If: ##\hat{H} \psi (x) = E \psi (x)## where E is the eigenvalue of the *disturbed* eigenfunction ##\psi (x)## and ##E_n## are the eigenvalues of the *undisturbed* Hamiltonian ##\hat{H_0}## and the *disturbed* Hamiltonian is of the form: ##\hat{H} = \hat{H_0} +{\epsilon} \hat{V}...
  41. W

    Solving a First Order Inhomogeneous ODE for a Regular LR Circuit with AC Voltage

    For a regular LR circuit (L and R in series) and with a AC voltage: I tried to derive the solution myself. https://www.dropbox.com/s/jmsu9j0vt91ze8x/LRcircuit.jpg So first I solved with undetermined coefficients, plugged them in, and then solved with Cramer's Rule. Then I added...
  42. S

    MHB How Do I Convert a Bernoulli Differential Equation to Linear Form?

    I know how to do a Linear First Order and I know how to do a Bernoulli (kind of). The kind of part may be why I'm having a problem. dy/dx+xy=xy^2 So I know in order for that to be a normal linear differential, that square on the last y has to go away somehow... I'm not sure how to do this...
  43. D

    Finding I(0)- and I(0)+ in First Order Circuit

    the question is to find I(0)- and I(0)+ the I is at the what I have attempted finding Req on the right side I eliminate the capacitor and Req = 12*6/(12+6) = 4 so Vc (0)- = Req/(Req+12) *18 = 9/2 T = Req*c= 4*1/12 = 1/3 so V(t) = 18/4 e^(-3T) so I (0)- = V(t)/12 = 3/8 e^(-3t)...
  44. I

    What is the significance of using a log scale in bode plots?

    How did they get the blue box? I know where they got the 0.5 inside the brackets from but not sure about the rest. The bode plot in my data book has log10(wt) as the x-axis..
  45. C

    First order phase transition/constancy of Gibbs

    Homework Statement a) Starting from the statement that total entropy (Ssystem+Ssurr) can only increase, show that G = U - TS +pV will attain its minimum value for a system in equilibrium with a fixed pressure and temperature reservoir. b)At atmospheric pressure, a particular substance is...
  46. C

    Where Does the δ(t) Term Come From in First Order Unit Step Response?

    I think I mostly understand how this works, and it makes intuitive sense. However, I'm a little bit confused by one step in the proving of this. On the second page of the attached PDF, there is this statement: x' + kx = (r/k + c2)δ(t) ... (followed by the cases of t<0 and t>0 What comes...
  47. K

    First order RC Circuit Table problem

    Homework Statement Hi I got this problem and have to fill out this table. Homework Equations node analysis time constant = RC ic(t)= C dVc(t)/dt The Attempt at a Solution I got few answers which i worked it out. i (0-) = 0 Vc(0-) = 1.84 Vr(0-) = i (0-) *...
  48. Choisai

    Why is the the first order useful?

    I've been looking into diffraction for AOLM and stuff like that, and these produce diffraction. Binary Spatial Light Modulators like Digital Micromirror Devices also produce diffraction. This diffraction is then focused and filtered using a pinhole. But, and here is the question: Why is always...
  49. F

    Differential Equations - first order

    Homework Statement a function has the feature that at any point, the product of its gradient and the x-cordinate is equal to the square root of the y-cordinate multiplied by 5. Part A: Write out a differential equation that describes the function Part B: If the curve passes through the point...
  50. MarkFL

    MHB Jaganmaya's question at Yahoo Answers regarding a first order ODE

    Here is the question: I have posted a link there to this thread so the OP can view my work.
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