Differential equation Definition and 1000 Threads

  1. B

    Strange Differential Equation: Solving a Radical Splitting ODE

    Homework Statement Solve the following differential equation, with the initial-value y(2)=2. y' = \sqrt{ \frac{1-y^{2} } { 1-x^{2} } } Homework Equations The Attempt at a Solution This is a strange ODE. It is continuous when either both |x|<1 and |y|<1 or when both |x|>1 and |y|>1. (Both of...
  2. A

    Differential equation 5y4y' = x2y' + 2xy

    Homework Statement Find the general solution of: 5y4y' = x2y' + 2xy 2. The attempt at a solution Well I've so far tried to simplify by making the equation really: (5y4-x2)y' - 2xy = 0 Now this will let us use exact equations such as: N(x,y)= 5y4-x2 and M(x,y)= -2xy...
  3. C

    Superficially simple vector differential equation problem

    Hi, I have the following vector differential equation (numerator layout derivatives): \frac{\partial e(v)}{\partial v}=\frac{1}{\beta} \frac{\partial w(v)}{\partial v} \Gamma^{-1} where both ##e(v)## and ##w(v)## are scalar functions of the vector ##v##, and where ##\Gamma## is a...
  4. N

    Need help with partial differential equation

    Homework Statement Given that z = √3x/y show that: Homework Equations ∂2z/∂x∂y = ∂2z/∂y∂x The Attempt at a Solution
  5. P

    Differential equation parametrisation with integrating factor

    Homework Statement Use parametrisation first, derive the equation including y and p = \frac{dy}{dx} and use the integrating factor method to reduce it to an exact equation. Leave the solution in implicit parametric form. (y')^{3} + y^{2} = xyy'The Attempt at a Solution I'm really lost at...
  6. L

    Differential equation: word problem

    1. In some chemical reactions, the rate at which the amount of a substance changes with time is proportional to the amount present. For the change of δ-glucono lactone into gluconic acid, for example, dy/dt= -.6y when t is measured in hours. If there are 90 grams of δ-glucono lactone present...
  7. L

    Differential equation: dy/dx = e^(8x-3y), y(0)=16

    1. The next differential equation I'm working on is this: dy/dx= e8x - 3y Alright, I thought to cancel out the e, we could take the ln of both sides...? ln(dy/dx) = 8x-3y Is this right so far? It doesn't seem like it's right because... well, how can you have an ln(dy/dx)?? Would...
  8. L

    Differential equation: 4sqrt(xy)dy/dx=1, y(1)=1

    The differential equation I'm working on is: 4(√(xy))dy/dx=1, y(1)=1 (√(xy)dy/dy)2 = (1/4)2 ((xy)dy/dx)*dx = (1/8)*dx (xy)dy = (1/8)dx (y)dy = (1/(8x))dx ...So I think this is right so far. Now I'm going to take the integral of both sides. ∫(y)dy = ∫(1/(8x))dx...
  9. T

    Finding the maximum value of x in a differential equation.

    Homework Statement I want to find the maximum value of x given that the differential equation relating x is: x' = 0.7548 - 599.49x^6 -2.4038x^2 - 0.12236x^1.5 Where x = 0 at t = 0. I have to do this with MATLAB using Euler's Method and here is my code: x = 0 a = 0 % initial t value b = 1000...
  10. N

    Which is the correct expression for the Differential Equation

    Homework Statement Which of the following is a correct expression for ∫1t(s-1)y'(s) ds I know the answer is: a) 1/2(t-1)2y(t) b) 1/2(t-1)2y'(t)+ (t-1)(y(t)-y(1)) c) (t-1)(y(t)-y(1)) d) (t-1)y(t)-∫y(s) ds Homework Equations The Attempt at a Solution I know the...
  11. N

    Which of the Following is a solution to the differential Equation

    Homework Statement Which fot he following is a solution to the differential equation: t2y" - 2ty' + 2y = 0 a)e-2tt3 b)et c)t d) t4 I have attached an image of the question Homework Equations The Attempt at a Solution I tried answer d first: y = t4 y' = 4t3...
  12. N

    The solution to the Differential Equation

    Homework Statement The Initial value problem: y' - (3/t)y = 0 y(1) = -10 Has the solution: I have attached an image of the question Homework Equations The Attempt at a Solution Firstly I found the integrating factor: u(t) = e∫-3/t dt u(t) = -3/t I plugged...
  13. T

    Differential Equation Help: As t approaches 0, y approaches

    Homework Statement http://edugen.wileyplus.com/edugen/shared/assignment/test/session.quest1886032entrance1_N10020.mml?size=14&rnd=1360201586591 (b) Solve the initial value problem and find the critical value a0 exactly. y = ? a0 = ? (c) Describe the behavior of the solution...
  14. G

    Green function Helmholtz differential equation, monodimensional limit

    The solution of the problem \left(\nabla^2 + k^2 \right)\psi(\mathbf{r})=f(\mathbf{r}) is, using green function \psi(\mathbf{r})=-\int G(\mathbf{r},\mathbf{r}_1) f(\mathbf{r}) where for the tridimensional case the Green function is...
  15. I

    Solve the integral of differential equation

    Homework Statement Solve the integral of differential equation ∫^{t}_{0} y(\tau) d\tau -\acute{y} (t) = t for t≥0 with y(0)=4 The Attempt at a Solution take laplace both sides \frac{Y}{s} - sY + 4 = \frac{1}{s^{2}} Y \frac{1 - s^{2}}{s} =\frac{1}{s^{2}} - 4 Y...
  16. S

    Separable differential equation

    Homework Statement I am asked to find a singular solution of the D.E. dy/dx = (xy+2y-x-2)/(xy-3y+x-3). I am first solving to find the general solution form of the D.E., and so far have it to: [(x+2)/(x-3)]dx = [(y+1)/(y-1)]dy From here, of course, you integrate both sides, but I am...
  17. H

    Help with Differential equation

    A hemispherical bowl of radius a has its axis vertical and is full of water. At time t=0 water starts running out of a small hole in the bottom of the bowl so that the depth of water in the bowl at t is x. The rate at which the volume of water is decreasing is proportional to x. Given that the...
  18. M

    Eliminating Arbitrary Constants: Solving the Differential Equation

    Homework Statement From the differential equation by eliminating the arbitrary constant from the equation (y - b ) ^2 = 4 (X-a ) http://www7.0zz0.com/2013/02/02/21/747681463.png
  19. Fernando Revilla

    MHB Norwin Dole's question at Yahoo Answers about a differential equation

    Here is the question: Here is a link to the question: How to obtain the general solution of ye^(2x) dx = (4+e^(2x))dy? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  20. P

    Solving time dependent differential equation and plotting

    Hi i have the differential equation \frac{d^{2}}{dt^{2}}X(t) +(A+B\frac{sin^{2}(mt)}{mt})X(t) I have tried by hnd to solve this and am getting knowhere does anyone know how to solve it and then plot X against t (where the constants A, B and m will be arbitrarily added), possibly using maple? I...
  21. Fernando Revilla

    MHB Non homogeneous linear differential equation

    I quote an unsolved question posted in MHF (November 7th, 2012) by user NumberMunhcer.
  22. T

    Is the Black-Scholes equation a differential equation?

    Hi everyone, first post. To anyone who has had experience with the background of the Black-Scholes equation used in finance to price options based on underlying assets (wiki here), I have just one simple question to ask regarding a research paper I must write. Is this equation a stochastic...
  23. P

    Unusual Solution to Riccati Differential Equation with ln x Particular Solution

    Homework Statement This is a Riccatti Equation which my answer is very weird after i solved it.. dy/dx+2y^2=(y/x lnx)+2(ln x)^2 where y=ln x is a particular solution Homework Equations The Attempt at a Solution i first let y=ln x+ 1/w and dy/dx=1/x-1/w^2 and substitute y and...
  24. E

    Differential equation dv/dt = 9.8 - v/5, v(0) = 0

    A falling object satisfies the initial value problem: dv/dt = 9.8 - v/5, v(0) = 0 1.Find the time that must elapse for the object to reach 98% of its limiting velocity. answer: t = 19.56, and for completeness, v = -49e-t/5 + 49 2.How far does the object fall in the time found in part a...
  25. S

    Differential Equation Involving Newtons Law of Motion

    Homework Statement mv'=-gm-kv Find the position function using the initial coniditions of t=0 for all Constants Homework Equations Reverse product rule The Attempt at a Solution My attempt is on my white board. Its attached as a picture.
  26. D

    Engineering RLC circuit - Differential equation - Stationary current calculation

    Homework Statement I'm decent with differential equations for RLC circuits, and I KNOW the stationary current will be zero, but I need help to work it out mathematically, because my maths gets me -2.4A (...) L: 0.05H C: 0.04F R: 3 Ω U (source) = 1 V I've got the transient solution: c1e-10t +...
  27. B

    Brachistochrone Differential Equation

    The first part of this problem asks me to solve the following for y' : \left( 1 + {y'}^2 \right)y = k^2 So I have: 1 + {y'}^2 = \frac{k^2}{y} {y'}^2 = \frac{k^2}{y} - 1 y' = \sqrt{{\frac{k^2}{y} - 1}} Then I am asked to show that if I introduce the following: y = k^2 \sin^2t Then...
  28. P

    How to Solve a Non-Exact Differential Equation with an Integrating Factor?

    the problem is (x+x^4)dy+y(y^3-x^3)dx=0 well I know that this is not a separable equation, homogenous equation or an exact equation...so i try to solve it by treating it as a non exact DE by finding out the integrating factor...but the both IF come out in term of x and y which involve 2...
  29. D

    Help with this separable differential equation

    The problem is dx/dt = (x+9)^2. This is separable so I made it dx / (x+9)^2 = dt. The only method I can think of using for something like this is partial fraction, but I can't get it to work with A/(x+9) + B/(x+9). Can anyone find a method that works?
  30. R

    Differential Equation First Order Linear

    Homework Statement Solve the following differential equation: y*e^(x^2)*dy/dx=x+xy Homework Equations y'+P(x)*y=Q(x) The Attempt at a Solution I tried to modify the equation to match the first order linear one, and I got: e^(x^2)*dy/dx=x/y+x (divided everything by y), but...
  31. U

    Solving a First Order Differential Equation with Initial Conditions.

    Homework Statement Solve the initial value problem: t(dy/dt)+8y=t^3 where t>0 and y(1)=0 Homework Equations None? The Attempt at a Solution It's a linear equation, so rearranged to dy/dt+8y/t=t^2. Took the integrating factor e^(∫8/tdt)=t^8 and multiplied through...
  32. I

    First order differential equation question

    The problem is : dy/dx=(x(x^2+1))/4y^3 when y(0)=-1/√2 This is my work so far: ∫4y^3dy=∫x(x^2+1)dx (y^4)/2=((x^2+1)^2)/2+c The answer from the textbook is y=-(√(x^2+2)/2) As you can see, my work will never equal the textbook answer when you put it in the y= stuff form. What did I do wrong?
  33. A

    What is the Correct Approach for Solving This Differential Equation?

    Homework Statement y = 2xy' + y(y')2 ; y2 = c1(x + c1/4) Homework Equations So far I've gotten the second equation to be: y = (c1x + c12/4)1/2 I was then going to take the derivative of that equation and plug them into the first equation after setting it to zero. Is that the...
  34. C

    Boundary Conditions and Solutions to Differential Equations

    Homework Statement Show that f(x) = A exp(σx) + B exp(-σx) is a solution to the following differential equation: f''(x) = (σ^2)f(x) where A, B, and σ are constants. What if a boundary condition is included that f(-∞) = 0? Homework Equations differential equation: f''(x) =...
  35. W

    Matrix differential equation for rectangular matrix

    Given a matrix differential equation (system of equations?) of the form: \textbf{X}^{\prime}(t) = \textbf{AX}(t) (where X is a complex matrix, t is real scalar and A is always a square and normal real matrix) I am able to find (e.g. here) that a general solution for square \textbf{X} is...
  36. marellasunny

    Number of parameters for a nonlinear differential equation

    Take for example a system \frac{dx_i}{dt}=(x_i,t,a,b,...) i-number of state equations. What would be the maximum number of parameters permitted for this system of non-linear differential equations? Is it finally determined by the solution space?Is there a criteria for number of...
  37. C

    I'm starting to learn about differential equation

    Homework Statement Verify that the differential equation, {\frac{dy}{dx}} = 15 - {\frac{2y}{81+3x}} has the general solution y(x) = 3(81+3x) + C(81+3x)^{-2/3} 2. The attempt at a solution I've just learned about differential equations, so I'm probably missing something very...
  38. I

    Separable Differential Equation Question

    Homework Statement dy/dx = (y^2 - 1)/ (x^2 - 1) with initial condition y(2) = 2 Why is y = 1 and/or y= -1 not solutions? Homework Equations The Attempt at a Solution I am actually able to solve this differential equation but when I separate the equation according to x and y...
  39. M

    Numerically Solving a Second Order Differential Equation Using C

    Homework Statement The Second Order Differential Equation is: x''-u(b^2 + x^2)x'+x=0 Initial Conditions are: x(0)=1 x'(0)=0 It is to be numerically solved for 0<=t<=500. The specific numerical method to be used isn't specified, but it must be programmed into c. As a means to check the...
  40. H

    How are partial differential equations used to model physical systems?

    Plese give me silminer simple example or anther example on this case or explein the steps
  41. S

    Is This Differential Equation Non-Exact in Non-Simply Connected Regions?

    I try to show, that equation \frac{-y}{ x^{2}+y ^{2} } + \frac{x}{ x^{2}+y ^{2}}y'=0 is not exact in \mathbb{R^{2}} \setminus \{(0,0)\}. It's obvious that I have to use the fact, that the set is not simply connected, but I don't know how to do it.
  42. J

    Can This Differential Equation Be Simplified or Solved Numerically?

    I have the following equation \frac{\partial}{\partial y}\left(y\frac{dm}{dx}+m\frac{dy}{dx}\right)-\frac{dm}{dx}=0 where m is a function of y (say m=f\left(y\right)) and y is a function of x (say y=g\left(x\right)). Are there any conditions under which \frac{dm}{dx} becomes identically...
  43. A

    Rayleigh's differential equation

    In Rayleigh's DE : http://www.wolframalpha.com/input/?i=rayleigh+differential+equation What does mu stand for?
  44. J

    How to integrate this partial differential equation

    I have the following equation \frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0 where y is a function of x and m is a function of y. If I integrate this equation first with respect to y should I get a function of x as the constant of integration (say C\left(x\right)) or it is just...
  45. B

    Differential equation with only the trivial solution

    Homework Statement Find a differential equation with its only (complex-valued) solution being y=0Homework Equations The Attempt at a Solution I believe that there is no DE having only y=0 as its solution, but frankly I am not sure if this is the case. I would like to know whether or not this is...
  46. J

    Nonlinear second order differential equation

    What is the solution of the follwoing differential equation \frac{\partial^{2}y}{\partial x^{2}}-ay^{-1}\frac{dy}{dx}=0 where a is a constant.
  47. J

    Why Equate Differential Equations to Zero?

    What is the logic behind equating differential equations to zero? For example the equation y''-5y'+6y=0 Because it can just as easily be written y''-5y'=-6y I am interested in the meaning of why if we sum y''+(-5y')+6y equals zero. What is the relationship of its second derivative, first...
  48. J

    Differential equation selection and linear transformations

    This may be vague, so I apologize. I am interested in applied mathematics, so my question is about the process a scientist or engineer uses to determine what differential equation to use for a non-linear process. I am not familiar enough with describing non-linear processes to be able to...
  49. E

    Does this differential equation have a closed form?

    I was busy doodling and basically ended up constructing this differential equation: p'(t)=c(t)p(t)-c(t-T)p(t-T) Obviously I've dealt with eq's like p'(t)=c(t)p(t) but I'm getting stuck because of the second term. Does this differential equation even have a closed form? Thanks.
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