Ordinary differential equation Definition and 97 Threads

Homework Statement dy/dx = 4e-xcosxThe Attempt at a Solution [/B] I've divided dx to both sides, and now have dy = 4e-xcosx dx I've then started to use intergration by parts to the right side with u = 4e-x and dv = cosx dx Leaving y = 4e-xsinx - ∫ -4e-xsinx dx Once again I used intergration...

i have read many of the answers and explanations about the similarities and differences between laplace and Fourier transform. Laplace can be used to analyze unstable systems. Fourier is a subset of laplace. Some signals have Fourier but laplace is not defined , for instance cosine or sine...

Homework Statement I stumbled upon a problem and i can't establish the ODE to solve it, from there on i believe i can solve the ODEs if they have regular analytical solving methods (translated from Spanish, will sound a bit weird) Car race, 2 pilots (a and b) participate in a drag race. They...

Homework Statement The website says this: "It is Linear when the variable (and its derivatives) has no exponent or other function put on it. So no y2, y3, √y, sin(y), ln(y) etc, just plain y (or whatever the variable is). More formally a Linear Differential Equation is in the form: dy/dx +...

Homework Statement y'=(x^2 +xy-y)/((x^2(y)) -2x^2)[/B]Homework EquationsThe Attempt at a Solution I know that really the only way to solve this one is to use an integrating factor, and make it into an exact equation. My DE teacher said that to make it into a exact equation you need to take...

Definition/Summary An nth-order linear ordinary differential equation (ODE) is a differential equation of the form \sum_{i=0}^n a_i(x)y^{(i)}(x)\ =\ b(x) where y^{(i)}(x) denotes the ith derivative of y with respect to x. The difference between any two solutions is a solution of the...

Homework Statement {g}'\left ( s \right )+\mu g\left ( s \right )={f}'\left ( -s \right )+\mu f\left ( -s \right ) Integrate up to get g\left ( s \right )=-f\left ( -s \right )+2\mu e^{-\mu s}\int_{-s}^{\infty }e^{-\mu {s}'}f\left ( {s}' \right )d{s}' Homework Equations As above...

I am trying to solve a homogeneous, first-order, linear, ordinary differential equation but am running into what I am sure is the wrong answer. However I can't identify what is wrong with my working?! $$\frac{dy}{dx}=\frac{-x+y}{x+y}=\frac{1-\frac{x}{y}}{1+\frac{x}{y}}.$$ Let $z=x/y$, so that...

Dear All, I have following first order nonlinear ordinary differential and i was wondering if you can suggest some method by which either i can get an exact solution or approaximate and converging perturbative solution. \frac{dx}{dt} = 2Wx + 2xy - 4x^{3}\frac{dy}{dt} = \gamma \, (x^{2} -...

Hi, The definition (see attachment) says that f(x) is a solution to the differential equation if it satisfies the equation for every x in the interval. Assuming that I have a differential equation that I want to solve and the D.E. has an interval I_1, and I've come up a solution with...

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

Homework Statement Find the ODE of the following (1) du/dy = -u (2) d^2u/dxdy = -du/dx Homework Equations For question 1, the answer is u= A(x)e^(-y) while for question 2, the answer is u= e^(-y)(B(X) + c(Y)) The Attempt at a Solution I've already solved the question, but...

hii, how to solve this differential equation: A*(dT(x)/dx)(1873.382+2.2111T(x))=90457.5-2.149*10^-10* (T(x))^4 where A is a constant Thank you

Homework Statement Homework Statement Solve \frac{dz}{dt} + 3 t e^{t+z} = 0 Homework Equations None that I can think of... The Attempt at a Solution "Rearranging" the given question, we get: \int \frac{dz}{e^z} = -3\int t e^t dt -e^{-z} = -3 \left( t e^t - e^t \right)...

Homework Statement x2y"-(x2+2x)y'+(x+2)y=0 known solutions: y1(2)=2 y1'(2)=1 y2(2)=2e2 y2'(2)=3e2 Determine the wronskian Homework Equations yc=C1er1x+C2er2x I also know how to find the wronskian via a determinant The Attempt at a Solution I have tried to divide out...

Homework Statement Here is an example from the book: https://dl.dropbox.com/u/64325990/MATH%20255/EX%204.PNG Does anyone know why they chose t to be equal to 0? Thanks!

Homework Statement Find the appropriate equation. Homework Equations So there we have the ordrinary differential equation \frac{d M}{dt}=k_1M-k_2(1-M)=A\exp \left (-\frac{E}{T} \right )M-B\exp \left ( -\frac{F}{T} \right )(1-M) The goal is to solve the differential equation. It...

I was trying to solve a calculus problem (about the equation of the curve traced by a dog chasing a postman) and I came across the following equation. I would like to know how to solve it. \frac{w}{v}(1-\frac{y(x)y''(x)}{{y'(x)}^{2}})=\sqrt{1+{y(x)}^{2}}-\sqrt{1+{C}^{2}} Thanks.

Hi there, I've having problems solving a particular nonlinear ODE. Any help/suggestions will be highly appreciated. The nonlinear ODE is: v[t]*v'[t] + (4*v[t])/(t^2 - 1) = t/(t^2 - 1) Thank you.

Homework Statement I haven't done ODEs in a few years and I am trying to do this equation: m_{Hg}C_{p,Hg}\frac{dT_{Hg}}{dt} = Q Q = hA(T_{air} - T_{Hg}) T_{Hg}(t = 0) = 20 I need to find T_{Hg}(t=590) Homework Equations The Attempt at a Solution h, A, m_{Hg}, C_{p,Hg}...

Hi! I have a differential equation coming from Boltzmann transport equation which is a bit complicated and should be solved numerically instead of analytically. I managed to get a plot using Runge-Kutta with software Derive. The equation is in the second attachment. In the papers of my...

Hi guys! Attached is the differential equation that I want to solve both numerically and analytically, numerically done. But analytically what method could I use? There is so many methods in differential equations. Please advice on this. Thank you very much

Homework Statement For t\in\mathbb{R}, let: A=\left[\begin{array}{ccc} -1 & 0 & 0\\ 0 & 2 & 2t\\ 0 & 0 & 2\end{array}\right] Get the solution for the general equation: X'=A(t)X Homework Equations The Attempt at a Solution I done many of these problems, all with constant...

Problem: y'+2y=4(x+1)2 ----> y=5e-2x+2x2+2x+1 1. What the Order of the ODE? It's 1st order 2 How do you check whether a particular function solves an equation? If you solve y'+2y=4(x+1)2 and make it y=5e-2x+2x2+2x+1. I want the whole solution... thanks...

Homework Statement Find the Particular Solution to the differential Equation satisfying the initial conditions. y''+7y'+10y= -30 y(0)= 3 y'(0) = -27Homework Equations Characteristic Equation for Homogenous Solution y''+7y'+10y=0 roots are -2 and -5 General Solution is C1e^-2t + C2e^-5t...

Homework Statement y' + Ay2 = B A & B are constants and y is a function of x Find the general solution to the differential equation. (Find y(x)). Homework Equations The Attempt at a Solution This differential equation came up when I was trying to solve a problem in...

Homework Statement I need to find a general function y(x) such that: \dot y(x) - 2y(x) = y^2(x)-3 Homework Equations The Attempt at a Solution I tried dividing the equation by y^2-3 and turn it into a Bernoulli differential equation, but that didn't work. The equation seems...

Homework Statement Note: Here your solution is implicitly defined, i.e. you can not rearrange the solution to get an explicit expression for y. Therefore you need to enter your solution as an equation. You should enter your solution in the form f(x,y) = constant where you have determined both...

How, if possible, could I solve the equation: x''x=((x')^2)/2? Thanks.

i have a second order ordinary differential equation of f(x): f''+(E-A(A+1)/x^2)f=0, where A is a positive integer, E is a real constant the domain is [0, \infty). the boundary condition is f(x=0)=0 since this is a linear equation, i only need to determine f up to a overall constant...

why is the 4th order Runge -Kutta method widely used than the 2nd or 3rd,for solving ordinary differential equations?

i have problem to find the solution for : (3x3y+2xy+y3)+(x2+y2)dy/dx=0 i have tried the exact equation method : (3x3y+2xy+y3)dx+(x2+y2)dy=0 thus M(x,y)=(3x3y+2xy+y3) and N(x,y)= (x2+y2) then deltaM/deltay=3x3+2x+3y2 and deltaN/deltax=2x Since deltaM/deltay does not equal to...

Homework Statement I am given dy/dt -2yt = 1 and y(t) = (e^(t^2))[e^(-s^2)ds] + e^(t^2) integrate from t to 0 within the brackets. Homework Equations The Attempt at a Solution I know that the derivative of y(t) would equal e^(t^2) However I do not know how I am supposed to solve...

What ordinary differential equation? Simple answer is needed! Homework Statement instead [delta] i will use 'd'. in these two example, what kind of ordinary dif. eq. are implied by the methodd of separation of variables. first one is; du/dt=(d^2u)/(dx^2) - 5 du/dt and other one is...

Homework Statement Given the Second-order nonlinear ordinary differential equation x''(t)=1/(x(t)^2) Find x(t).Homework Equations I tried use Laplace transforms, and solving it using linear methods but that is not useful.The Attempt at a Solution I tried to find t(x) and got to...

Homework Statement y' = \sqrt{(1-y^2) } Initial condition y(0) = 0 a) Show y = sinx is a solution of the initial value problem. b) Look for a solution of the initial value problem in the form of a power series about x = 0. Find coefficients up to the term in x^3 in this series. Homework...

Homework Statement Solve the differential equation: y' = 8sin(4yt) ; y(1) = 4 Homework Equations The Attempt at a Solution The integrating doesn't apply because I can't get the equation into: y' + p*y = f(x) form Also, I have tried separating variables, but I can't get the y inside of the...

Homework Statement dy/dx = (x+3y)/(3x+y) I have to solve the given differential equation by using an appropriate substitution... The Attempt at a Solution I used algebra to make the equation (3x+y)dy - (x+3y)dx = 0 then made x = vy and dx = vdy + ydv. then plugged into get...

Homework Statement Find the general solution of the differential equation, y' + y = be^(-λx) where b is a real number and λ is a positive constant. Homework Equations y' + P(x)y = Q(x) Integrating factor: e^(∫P(x) dx) The Attempt at a Solution Let P(x) = 1, Q(x) =...

Hi all. Can the general solution of a linear ordinary differential equation be expressed in terms of its initial conditions? It seems that I have seem this kind of representation. It makes "some sense" to me but I hope to know if there is some "proof" or explanation of why it can be? To be...

I have been looking though Ince (Ordinary Differential Equations), nice book. I enjoyed solving this problem: 6) pp. 157 Integrate the system x*x''-y*y''=0 x''+y''+x+y=0 [Edinburgh, 1909.] we may assume x and y are twice differentiable functions defined everywhere from reals to reals...

Any help with solving this first-order nonlinear ODE would be greatly appreciated! I do believe that an explicit solution exists. Homework Statement dy/dt = 1/(4t^2) + 1/2 + 1/2*y/t - 1/(2t)*((1+4ty)^(1/2)) I was led to believe that it could be solved by turning it into a linear...

Homework Statement What is the general solution to the following ODE F=X''m where F and m are both constants Homework Equations The Attempt at a Solution I got X=(k/2)t^2 + C I got this from F/M being just another constant K, and X'' being (d^2 X)/(dt^2) so you just...

Homework Statement Obtain the general solution: (1 - x)y' = y^2 Homework Equations The Attempt at a Solution (1 - x)\frac{dy}{dx} = y^2 (1 - x)dy = y^2dx \frac{dy}{y^2} = \frac{dx}{(1-x)} integrating both sides: i used ln on the constant at the right side -\frac{1}{y}...

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Homework Statement the equation of motion for a damped harmonic oscillator is d^2x/dt^2 + 2(gamma)dx/dt +[(omega0)^2]x =0 ... show that x(t) = Ae^(mt) + Be^(pt) where m= -(gamma) + [(gamma)^2 - (omega0)^2 ]^1/2 p =-(gamma) - [(gamma)^2 - (omega0)^2 ]^1/2 If x=x0 and...

what is the word ordinary mean? Why is it called so. Am i correct to say that the solution of a differential equation is got by integrating that equation.