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. D

    MHB Understanding the First Order Prototype Solution in Time Domain

    Consider the first order prototype, \[ \frac{dy(t)}{dt} + \frac{1}{\tau}y(t) = f(t),\] driven by a step function, \[ f(t) =...
  2. MarkFL

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

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

    Solving First Order Differential Equation

    Homework Statement I have been trying to solve this equation but keep coming to the same solution, which according to my book is not the correct one. Is anyone able to point out what I am doing wrong? \frac{dy}{dt}-\frac{1}{2}y=2cos(t) The Attempt at a Solution To solve, use...
  4. J

    Where did I go wrong with my solution to this first order ODE?

    Homework Statement Can anyone point out where I have gone wrong with this? Verify that the given function is a solution of the differential equation. y' -2ty =1 y= e^{t^2}\int^t_0 e^{-s^2}ds+e^{t^2} The Attempt at a Solution The steps I have taken are the following: i)...
  5. T

    First order differential eqn dy/dx + Py = Qy^n

    show that the substitution z = y^-(n-1) transforms the general equation dy/dx + Py = Qy^n, where P and Q are functions of x, into the linear equation dz/dx - P(n-1)z = -Q(n-1). (Bernoulli's equation) Well, I looked up Bernoulli's stuff on internet, found the usual air flow equation but not...
  6. MarkFL

    MHB Clare's question at Yahoo Answers regarding a first order linear IVP

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

    A general methodical way to solve all first degree first order

    Is there a single, general, solution guaranteeing method that can be applied to any first degree first order differential equations? I know there are a lot of techniques or should I say categorizations for solving these types of equations, like linear, homogeneous, Bernoulli equations...
  8. D

    First order differential equations

    Homework Statement Consider the first order differential equation \frac{dx(t)}{dt} + ax(t) = f(t), x(0) = x_{0}, t\geq0 Suppose the "input signal" f(t)=e^{-t}, t\geq0 . (a) Find the solution to the equation. Find a condition on the parameter a so that the solution of the (forced) system...
  9. G

    Problem with Wick's theorem at first order

    Hey there, first post here! I've been struggling with a detail in Second Quantization which I really need to clear out of my head. If I expand the S-matrix of a theory with an interaction Hamiltonian H_I(x) then I have S - 1= \int^{+\infty}_{-\infty} d^4 x H_I(x) +...
  10. MarkFL

    MHB Amber's questions at Yahoo Answers regarding linear first order ODEs

    Here are the questions: I have posted a link there to this thread so the OP can view my work.
  11. C

    First order non-linear differential equation

    Homework Statement Hello, I was given an extension problem in a Dynamics lecture today and am struggling to solve it. It is a simple scenario: a particle of mass m is accelerating due to Galilean gravity, but is subject to a resistive force that is non-linear in the velocity of the particle...
  12. S

    MHB Differential eq of first order and higher degree

    How to proceed to find the general and singular solution of the equation 3xy=2px2-2p2, p=dy/dx
  13. T

    MHB Non-linear first order differential equation question

    Kindly solve it and i need help to understand NON LINEAR Questions
  14. P

    First order in time=> time cannot go backwards ?

    First order in time=>"time cannot go backwards"? I have had numerous professors mention, but not explain, the differences between PDEs that are second order and first order in time. For example, in the regular wave equation, they say that "time can go backwards," or something to that effect. In...
  15. MarkFL

    MHB Owen b's question at Yahoo Answers regarding a first order homogenous ODE

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

    General Solution of 2y'+y-(2y')*ln(y')=0

    Homework Statement Find the general solution of 2y' + y - (2y')*ln(y') = 0 Homework Equations The Attempt at a Solution I have no idea how to deal with this i mean none of the first order techniques work and it's mainly because I don't know how to deal with the ln(y'). I tried seperating...
  17. M

    Solving Linear First Order PDE with Initial Conditions

    Homework Statement Mod note: Pasted the OP's correction into the original problem. Solve xe^z\frac{\partial u}{\partial x} - 2ye^z\frac{\partial u}{\partial y} + \left(2y-x \right)\frac{\partial u}{\partial z} = 0 given that for x > 0, u = -x^{-3}e^z when y=-x Homework Equations...
  18. N

    MHB Recasting/Reducing ODEs of order n to first order

    Could someone please provide a worked solution for me. I think that is the only way I will understand this. It was covered very vaguely in our lectures and my notes start talking about vectors and using co-domain notation which is very frustrating! 1. $y''(x) = x + y'(x) + e^{y(x)}$ with...
  19. MarkFL

    MHB Hank's question at Yahoo Answers regarding a first order linear IVP

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  20. M

    How to show this equivalence in first order language ?

    Here is the question in attachment , I make it as the site don't support LaTeX I think! https://www.physicsforums.com/attachment.php?attachmentid=63439&stc=1&d=1383093152
  21. F

    MHB Why Isn't y Treated as a Constant in the Product Rule?

    Find the gernal solution of cosx\frac{dy}{dx}+(sinx)y=1 So \frac{dy}{dx}+\frac{sinx}{cosx}y=\frac{1}{cosx} \frac{dy}{dx}+tan(x)y=csc(x) therefore P(x)=tan(x) Let \mu (x) = e^{\int P(x) dx}=e^{\int tan(x) dx} =\frac{1}{cosx} multiply both sides of the equation by integrating factor...
  22. D

    MHB First Order Non-Linear Ordinary D.E.

    Hello people, I couldn't solve the given D.E by using exact d.e & substitution method :( Thanks in advance. (x*y*sqrt(x^2-y^2) + x)*y' = (y - x^2*(sqrt(x^2-y^2) ) gif file of d.e can be found in the attachments part.
  23. S

    Solving a First Order Linear PDE

    Good day. I was wondering if you could help me solve this first order linear partial differential equation: [∂δ]/[/∂t] = [ρg]/[/μ] δ^2 [∂δ]/[/∂z]. The solution for this is: δ(z, t) = √[μ z]/[/ρg t]. I don't really understand how the PDE became like this. If you could show the...
  24. mnb96

    Question on Taylor expansion of first order

    Hello, according to my textbook, the Taylor expansion of first order of a scalar function f(t) having continuous 2nd order derivative is supposed be: f(t) = f(0) + f'(0)t + \frac{1}{2}f''(t^*)t^2 for some t^* such that 0\leq t^* \leq 1 Quite frankly, I have never seen such a formulation...
  25. B

    First order partial wave eqaution, one boundary and one initial condit

    Homework Statement Solve \frac{\partial{w}}{\partial{t}} + c \frac{\partial{w}}{\partial{x}} =0 \hspace{3 mm} (c>0) for x>0 and t>0 if w(x,0) = f(x) w(0,t) = h(t) Homework Equations The Attempt at a Solution I know how to solve for the conditions separately and that would give...
  26. C

    MHB First Order Nonlinear Ordinary Differential Equation

    Hello, can you guys help me please with this differential equation from Demidovitch book, is to find the solution transforming to polar coordinates :
  27. N

    MHB First Order Differential Equations, given initial value....

    I'm having trouble with this problem... I am almost certain that I have the first part correct which is solving the first order DiffEQ using an integrating factor. I think that I am computing the constant incorrectly. I have followed all steps, including the similar problem given on WileyPlus...
  28. W

    First Order Differential Equation

    Homework Statement Find the general solution to the following differential equation. dy/dx = 2x( (y^2) + 1) Homework Equations The Attempt at a Solution I got all x terms on one side and all y terms on the otherside 2x dx = 1/( (y^2) + 1`)dy integrate x^2 + c =...
  29. H

    How Do You Solve for Position x(t) Given a Force Dependent on Velocity?

    A particle of mass m is subject to a force F(v) = bv^2. The initial position is zero, and the initial speed is vi find x(t) so far m*dv/dx*v = -bv^2 m*dv/dx = -bv integral m/-bv*dv = integral dx m/-b*ln(v) + a = x + b What do I do with the constants? i thought i was suppose to put...
  30. F

    MHB Verifying solution to first order differential equation

    Verify the indicated function y=phi(x) is an explicit solution of the given equation. Consider the phi function as a solution of the differential equation and give at lease one interval I of definition. (y-x)y'=y-x+8 where y=x+4\sqrt{x+2} So the derivative is y'=1+\frac{2}{\sqrt{x+2}} and the...
  31. MarkFL

    MHB Thingsto Do's question at Yahoo Answers regarding a first order homogeneous IVP

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  32. I

    Solving a First Order DE: y'+ycot(x)=cos(x)

    Homework Statement y'+ycot(x)=cos(x) Homework Equations The Attempt at a Solution First I found the integrating factor: \rho (x)=e^{\int cot(x)dx}=e^{ln(sinx)}=sinx Plug into the equation for first order DE... \int \frac{d}{dx} ysinx=\int cosxsinx dx End up with...
  33. alane1994

    MHB Modeling with a First Order Equation

    Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200L of dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 L/min, the well-stirred solution...
  34. C

    Convert sentences into First Order Logic

    Hello there, I have 3 sentences. They are: 1) If someone is not in the class then that person is either ill or lazy. 2) Ill people do not go for shopping. 3) The class teacher noticed that James is not in the class but she has seen James come out of the Candy...
  35. B

    First order perturbation for hydrogen

    Homework Statement Assume that there is a deviation from Coulomb’s law at very small distances, the Coulomb potential energy between an electron and proton is given by V_{mod}(r)=\begin{cases} -\frac{e^{2}}{4\pi\varepsilon_{0}}\frac{b}{r^{2}} & 0<r\leq b\\...
  36. T

    PDE: Wave equation with first order derivative

    Homework Statement Solve using separation of variables utt = uxx+aux u(0,t)=u(1,t)=0 u(x,0)=f(x) ut=g(x) The Attempt at a Solution if not for the ux I'd set U=XT such that X''T=TX'' and using initial conditions get a solution. In my case I get T''X=T(aX'+X'') which is...
  37. F

    How do I find the Taylor series for a function with multiple variables?

    Homework Statement I required to make a perturbation expansion in ε of the function: Homework Equations A(X,y,z)=A(x-εsin(wy),y,z). X=x-εsin(wy) The Attempt at a Solution Solution: A(X,y,z)=A0(X,z)+ε[A1(X,z)+∂/∂XA0(X,z)]sin(wy)+o(ε^2) I get the terms A0(X,z) and ∂/∂XA0(X,z)sin(w,y) with the...
  38. A

    Open Loop Response of a car using a Basic First Order Model

    Homework Statement Car Dynamics f(t)→ \frac{\frac{1}{M}}{s+\frac{D}{M}}→y(t) Applied Force Velocity Homework Equations M=1,000 kg and D=1000 kg/s Where f(t) represents the input force and y(t) is the output velocity. M is the Mass and D...
  39. R

    First Order RC Circuit Analysis: Homework Equations and Attempted Solution

    Homework Statement Homework Equations vc(t) = vc(∞) + [vc(0+) - vc(∞)]*e-t/τ (Voltage in a driven RC circuit) τ = RC (time constant for an RC circuit) The Attempt at a Solution I'm pretty shaky with these sorts of problems and am quite unconfident of my work here. Step...
  40. L

    Transformation question; first order shift of a scalar field

    Hi to all! I have the following transformation \tau \to \tau' = f(\tau) = t - \xi(\tau). Also I have the action S = \frac{1}{2} \int d\tau ( e^{-1} \dot{X}^2 - m^2e) where e = e(\tau) . Then in the BBS String book it says that $$ {X^{\mu}}' ({\tau}') = X^{\mu}(\tau)$$ and...
  41. B

    Using Lie Groups to Solve & Understand First Order ODE's

    Hey guys, I'm really interested in finding out how to deal with differential equations from the point of view of Lie theory, just sticking to first order, first degree, equations to get the hang of what you're doing. What do I know as regards lie groups? Solving separable equations somehow...
  42. MarkFL

    MHB Reid's question at Yahoo Answers regarding a first order separable IVP

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  43. Petrus

    MHB First order linear differential Equation

    Hello MHB, (x^2+1)y'-2xy=x^2+1 if y(1)=\frac{\pi}{2}What I have done: Divide evrything by x^2+1 and we got y'-\frac{2xy}{x^2+1}=1 we got the integer factor as e^{^-\int\frac{2x}{x^2+1}}= e^{-ln(x^2+1)} Now I get (e^{-ln(x^2+1)}y)'=e^{-ln(x^2+1)} and this lead me to something wrong, I am doing...
  44. S

    Finite size effects at first order phase transitions

    Hi. I am trying to understand some features related to the order of a phase transition. It is known that there are finite size effects in a finite system. The finite size scaling theory provides relations between some quantities with the length of the system L. At second order phase...
  45. K

    MHB Help rearranging a linear first order differential equation

    Hi I am trying to solve dy/dx = 3x^2-2x+2+(8/x *y) Can anyone show me how to rearrange to standard form as I am mightly confused :(
  46. MarkFL

    MHB Tab'z's questions at Yahoo Answers regarding a linear first order IVP

    Here is the question: Here is a link to the question: Can someone help me solve this: y'+tan I have posted a link there to this topic so the OP can find my response.
  47. MarkFL

    MHB Marcus Right's question at Yahoo Answers regarding a first order homogeneus ODE

    Here is the question: Here is a link to the question: Homogenous Differential Help with equation? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  48. P

    First order linear differential equation

    Homework Statement dy/dt = k*y*ln(y/M), where M and k are constants. Show that y = Meaekt satisfies the above equation for any constant a. Homework Equations y' = ky y = P0ekt The Attempt at a Solution Taking the derivative of y, I get: (Meaekt)*(aekt)*k which is, ky*aekt ..and I'm...
  49. F

    How can I solve a first-order non-linear ODE?

    Hi! I'm having a lot of trouble solving the following ODE: dx/dt = A - B*sin(x) where A and B are constants. My ODE skills are a bit rusty, and I wasn't able to find anything on the Internet that could help me, so could someone please show me how to solve for x in terms of t? I've...
  50. O

    Periodic Solution to FIrst Order ODE Proof

    Homework Statement Consider the differential equation x' = f(t,x) where f(t,x) is continuously differentiable in t and x. Suppose that f(t+T,x) = f(t,x) for all t Suppose there are constants p, q such that f(t,p) > 0, f(t,q) < 0 for all t. Prove that there is a periodic solution...
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