Ode Definition and 1000 Threads

Hi all, I have a nonlinear ODE in the following form: a x'' + b |x'|x' + c x' + d x = y where x and y are functions of time and a,b,c and d are constants. As far as I can tell the only way to solve this is numerically, something I've managed to do successfully using a Rung-Kutta scheme...

Homework Statement Find a solution of the IVP \frac{dy}{dt} = t(1-y2)\frac{1}{2} and y(0)=0 (*) other than y(t) = 1. Does this violate the uniqueness part of the Existence/Uniqueness Theorem. Explain. Homework Equations Initial Value Problem \frac{dy}{dt}=f(t,y) y(t0)=y0 has a...

Homework Statement We have y'' + 4y' + 4y = 0 ; find the general solution. Homework Equations Reduction of Order. The Attempt at a Solution So when determining the roots of the characteristic equation, -2 was a double root, and therefore we can't simply have c1e-2t + c2e-2t. So I thought...

Homework Statement Suppose u, v are two linearly independent solutions to the differential equation u''+p(x)u'+q(x)v=0. If x0,x1 are consecutive zeros of u, then v has a zero on the open interval (x0,x1) Homework Equations The Attempt at a Solution I'm trying to use the...

Homework Statement Two reservoirs are connected. Water drains from one reservoir to the other, governed by the following ODE: dh/dt= -k1*(h)^0.5 -k2*(h-H)^0.5 , H<0, k1,k2>0 Does an equilibrium exist? What happens in terms of Picard's Existence Theorem? Draw a phase diagram of possible h*...

Homework Statement Find general solution to: xy''+2y'+4xy=0 Homework Equations Frobenius Method or Bessel's Equation The Attempt at a Solution I know how to get the roots for this problem (which are r1 = 0 & r2 = -1). But not I don't know what to do with these roots. I know that...

I am getting this error in Mathematica from the code below: Computed derivatives do not have dimensionality consistent with the initial conditions ClearAll["Global`*"] \[Mu] = 398600; s = NDSolve[{x1'[t] == x2[t], y1'[t] == y2[t], z1'[t] == z2[t], x2'[t] == -\[Mu]*x1[t]/(x1[t]^2 +...

Hi everyone, I have an inhomogeneous Bernoulli type ODE given by u'(t) = \kappa u(t) + \ell(t) u^{\gamma}(t) + v(t),\ \ \ u(T)=b>0,...(1) where t\in[0,T],\ \ \gamma\in (0,1) . My concern is that how to prove the existence and uniqueness of the solution u(t) for all t\in [0,T]...

Homework Statement First time I've had to deal with ODEs, an I'm pretty confused. This SHOULD be a simple ODE for finding air resistance, that is only dealing with the y vector (up and down in this case) m\frac{dv_{y}}{dt}=mg-kv_{y} Homework Equations F=ma f=-kV The Attempt at a...

Here is the question: Here is a link to the original question: Solve this differential Equation: df/dy(t) + f(y) =sin(2y)? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hi everyone, Im looking for an autonomous first order ode that has the following properties. For dependent variable x: x(t=∞)=0 x(t=-∞)=0 and the function x(t) has one maximum. Any help would be great. Rgds...

Homework Statement Identify the region that the DE will have a unique solution. y' = \frac{y^2}{x^2+y^2} The Attempt at a Solution \frac{\partial f}{\partial y} = \frac{2x^y}{(x^2+y^2)^2} I'm a bit rusty with my domains, but here is what I've got. x: (-∞, -2) U (2,-∞) y...

Homework Statement Hi, Wondering if anyone can give me some help with reducing this 3rd order ODE to a first order problem, so it can be written in the form u' = f(u, t) Homework Equations The 3rd order ODE is: x'''(t) + x''(t) + 2x'(t) + 2x(t) = 2t^2 + 4t - 5; The initial values...

Homework Statement (y^2 + xy)dx - x^2dy = 0 The Attempt at a Solution Put it into derivative form. y^2 + xy - x^2 \frac{dy}{dx} = 0 \frac{dy}{dx} - \frac{y^2}{x^2} - \frac{xy}{x^2} = 0 \frac{dy}{dx} + \frac{-1}{x}y = \frac{1}{x^2}y^2 I recognized this as a Bernoulli equation...

I would like to solve the non linear ODE \frac{d}{dx}f(x)=a f(x)+ b f^3 (x) with the boundary f(0)=0\quad f(+\infty)=f_0 How to find analitical solution?

Dear All, What type of packages exists out there to the solution of the ODE equations in engineering especially for the M*X''+C*X'+K*X = F ; 2nd order equation, where none of the variables denoted as M, C, K and F are function of the time and are mass, damping, stiffness and force matrices...

Homework Statement basically solve \frac{d^{2}y}{dx^{2}} + 4\frac{dy}{dx} + 4y = cos2x Boundary conditions are y=0, dy/dx =1 at x=0 Homework Equations The Attempt at a Solution I am having trouble getting the coefficients to the solution. I got the complementary function as...

Question: Show that the system x'= x-y-x[x^2 + (3/2)y^2] y'= x+y -y[x^2 + (1/2)y^2] has at least one periodic orbit. I know that I need to apply Poincare-Bendixson Theorem. I can prove the first three points of it easily, but to create a trapping region, I believe that I need to...

Homework Statement I'm currently taking a course on ordinary differential equations. I am now reading through the lecture slides but I'm not really sure about the " factorising the equation " part onwards: Homework Equations The Attempt at a Solution I'm not sure what is...

Homework Statement Dear all, please help. I have tried this question and came up with strange numbers, my fortran is definitely not correct. Please help! When the effect of the air resistance is taken into account, the equation of motion for a particle of mass m falling vertically in a...

Hi. If I have a homogeneous ODE with constant coefficient system in the form of 2x2 matrix: X'=A X, A is a 2x2 matrix. How do I solve this using wolfram or matlab?

Homework Statement Solve the following systems by either substitution or elimination: dx/dt = y dy/dt = -x + cos(2t) Homework Equations I know the solution is: x(t) = c_1cos(t) + c_2sin(t) - 1/3cos(2t) y(t) = -c_1sin(t) + c_2cos(t) + 2/3sin(2t) The Attempt at a Solution x' = [ 0 1; -1...

Homework Statement \dot{ω_{1}} = λω_{2} +μ \dot{ω_{2}} = -λω_{1} Homework Equations λ and μ are real, positive constants ω_{1}(0) ≠ 0 ω_{2}(0) ≠ 0 The Attempt at a Solution I know that the general solution will be in the form ω1(t) = A sin ωt + B cos ωt + C ω2(t) = D sin...

Homework Statement I'm trying to understand the simplification of the general solution for homogeneous linear ODE with complex roots. Homework Equations In my notes, i have the homogeneous solution given as: y_h (t)= C_1 e^{(-1+i)t}+C_2e^{(-1-i)t} And the simplified solution is given as: y_h...

The ODE to solve via variation of parameters is ##(1-x)y''+xy'-y=(1-x)^2##. Knowing that ##e^x## and ##x## are solutions to the homogeneous ODE. Now if I call ##y_1=x## and ##y_2=e^x##, the Wronskian is ##W(y_1,y_2)=e^{x}(x-1)##. According to...

Homework Statement Find the general solution to ##A(x)y''+A'(x)y'+\frac{y}{A(x)}=0## where A(x) is a known function and y(x) is the unknown one. Hint:Eliminate the term that contains the first derivative. Homework Equations Not sure. The Attempt at a Solution So I don't really...

Homework Statement We have the equation: y'(x)^2+2 (x+1) \left(y'(x)+x\right)+2 y(x)+2 x=0 2. The attempt at a solution None. I don't even know how to proceed with this problem, except for, of course, expansion. I tried the factorization method, but no luck here. I have a feeling I...

Homework Statement I must solve ##y''+2y'+2y=e^{-t}\sin t##. I know variation of parameters might not be the fastest/better way to solve this problem but I wanted to practice it as I never, ever, could solve a DE with it. (Still can't with this one). Though the method is supposed to work...

Homework Statement Hello guys! I've never dealt with an ODE having 2 singularities at once, I tried to solve it but ran out of ideas. I must solve ##(x-2)y''+3y'+4\frac{y}{x^2}=0##. Homework Equations Not sure. The Attempt at a Solution I rewrote the ODE into the form...

Homework Statement Hello guys. I'm totally stuck at finding the solution to ##y'''-12y'+16y=32x-8##. Homework Equations Variation of parameters once I'm done with the general solution to the homogeneous ODE. The Attempt at a Solution First I want to solve the homogeneous ODE...

Hello there, I am solving numerically the ODE $$ \dot{y} = min \, (y, A) + B\, sin(t)$$ , A,B being constant. I obtain a very "wiggled" solution which is very fine to me actually, as it echoes the problem I am studying. However, as the numerical solution scheme is quite "rudimentary" I...

This is surely the simplest problem imaginable in DE, but it's been a few years and I'm having trouble recalling. The goal of my task doesn't necessitate relearning DE, so I thought I would take a shot at asking directly. Simply, I wish to express the time-dependent rate equation...

Homework Statement x d2y(x)/dx2 + dy(x)/dx + 1/4 y(x) Show that the solution can be obtained in terms of Bessel functions J0. Homework Equations Hint: set u = xa where a is not necessarily an integer. Judiciously select a to get y(u). The Attempt at a Solution I tried just...

Homework Statement Find the general solution of the ODE $$ y'' + 16y = 64x \cos x.$$ If ## y(0)=1, y'(0) = 0##, what is the particular solution? The Attempt at a Solution I am confident I can tackle this question, I really just want to check that my particular integral form is correct. I...

I have been thinking about numerical methods for ODEs, and the whole notion of stability confuses me. Take Euler's method for solving an ODE: U_n+1 = U_n + h.A.U_n where U_n = U_n( t ), A is the Jacobian and h is step size. Rearrange: U_n+1 = ( 1 + hA ).U_n This method is...

This is not homework, but rather me just trying to work a numerical analysis problem. I have a second order equation on the form m*y'' = a*y + n*x (no first derivative) How does one convert this? It's been years since I did this. Last I remember, one would start with substituting the...

Solve the differential equation: y(5)+12y(4)+104y(3)+408y''+564y'=0 where the (n) is the nth derivative. So it's a 5th order DE. Now I'm trying to find the roots: One of the roots is r = 0, which I obtain by factoring the equation into this form: r(r4+12r3+104r2+408r+1156) = 0...

Recently I was sent an ODE with the instructions to solve using the annihilator method which I have not used in over 15 years. This is my working, and I was hoping for feedback to see if I have correctly and efficiently applied the method. Here is my working: We are given the ODE: (1)...

Folks, I am trying to understand the balance of units for this eqn ## \displaystyle \frac{d^2}{dx^2}(E(x)I(x) \frac{d^2 w(x)}{dx^2})+c_f(x)w(x)=q(x)## where ##E## is the modulus of Elasticity, ##I## is the second moment of area, ##c_f## is the elastic foundation modulus, ##w## is...

Not sure if this topic belongs here, but here goes. Homework Statement From the AP physics C 1995 test there is a problem that gives the potential energy curve U(x). With F=-\frac{dU}{dx} in one variable, F(x)=-\frac{a}{b}+\frac{ba}{x^{2}} Where a and b are constants. Now I need to get...

Homework Statement Show that y(t) = (1/w) ∫[0,t] f(s)*sin(w(t-s)) ds is a particular solution to y'' +w2 y = f(t)where w is a constant. The Attempt at a Solution After wasting several pages of paper I have made virtually no progress. Obviously, substitution suggests you plug in y(t)...

How to covert this differential equation into a system of one order ODE? (require covert the equation into a system of 1st-order equations and solve by using ode23 in matlab) x^2*y''-2*x*y'+2*y = 0; y(1) = 4; y'(1)=0; solve for y(x) I tried to convert it get X' = AX in which X...

How to covert this differential equation into a system of one order ODE? x^2*y''-2*x*y'+2*y = 0; y(1) = 4; y'(1)=0; solve for y(x) I tried to convert it get X' = AX in which X = [y, z]' A = [0, 1; 2/x^2, 2/x]; But x exists in A, which cannot solve by dsolve in Matlab.

I'm sorry this is going to sound kind of confusing and vague at first but stick with me! I remember a physicsforum thread from long back in which a student posted a test they'd been given back where the instructor marked them off and they argued they were right. The test question was to solve...

Homework Statement Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α Homework...

Four days ago on mathhelpforum.com the user ssh [I don’t know if he the same as in MHB…] has proposed the following second order complete linear ODE… $\displaystyle y^{\ ''} – \frac{2+x}{x}\ y^{\ ’}\ + \frac{2+x}{x^{2}}\ y = x\ e^{x}$ (1) … and till now no satisfactory solution has been...

I was given the following equation to solve: x^2*y'' + x*y' + k^2*x^2*y = 0 B.C. y'(0)=0, y(1)=0 where k is just some constant. I am having a hard time removing the singularity created by the boundary condition at y' and not aware of a method how. Any advice would be greatly appreciated.

Homework Statement I'm pretty sure this is a typo? http://gyazo.com/802746486cc68852e5384d5a12aed596 Homework Equations See the image ^. The Attempt at a Solution I believe the theorem they're talking about, is that you can write the general solution of a second order ODE : L[y] = y'' +...

Hi all, I'm struggling with this question - I don't really know where to start. So far I have tried putting arbitrary values for 'a' into a quadratic auxiliary equation but using wolfram to calculate the roots gives me complex conjugates that I can't remember a thing about. Question as...

Suppose I have a really simple first order linear ODE like:$$\dot{\omega} = -k\omega$$ where k is some constant, ω(t) is a function of time that I want to solve for, and the overdot denotes the derivative w.r.t. time. This is really easy to solve, and we all know that with the initial condition...