Ode Definition and 1000 Threads

Dear all, I have problem to find the differential equation for my circuit shown in the attached picture. For input I have a current source, and the output is the voltage U (the voltage between the first and the ground node). I need the ODE to find the mathematical response of the system...

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Homework Statement A dynamical system has a response, y(t), to a driving force, f(t), that satisfies a differential equation involving a third time derivative: \frac{d^{3}y}{dt^{3}} = f(t) Obtain the solution to the homogeneous equation, and use this to derive the causal Green's function...

Fint the exact solution of the system dy/dt = -15y-25z dz/dt=-47y-85z with inital condition y(0)=2, z(0)=5 either by writing the equation in matrix form as dx/dt =AX where x=(y z) and diagonalising the matrix A, or otherwise. Using fortran programming with second order adam bashforth...

Adapt the fortran programming using second order adams bashforth method to generate a numerical solution of the Lorenz system: dx/dt =-10x+10y dy/dy=28x-y-x*z dz/dt= x*y- (8/3)*z with initial condition x(0)=y(0)=0, z(0)=2 slightly perturbed. Plot x and z against t runs from 0 to 15, and also z...

In Bessel's ODE x^{2}y''+xy''+(x^{2}-\nu^{2})y=0, why must \nu not be less than zero? I have looked it up, but I do not find a satisfying answer anywhere.

Hello, I am working on a research problem and I am not sure whether or not I will be able to figure this out in a suitable amount of time. I have never solved a single elliptic integral and they do seem non-trivial to gain an understanding of (most of the books I've glanced at assume a very...

Homework Statement y''+6y=f(t), y(0)=0, y'(0)=-2 f(t)= t for 0≤t<1 and 0 for t≥1 Homework Equations The Attempt at a Solution L{y''}+6L{y}=L{t}-L{tμ(t-1)} where μ(t-1) is Unit Step Y(s)=L{y} sY(s)-y(0)=L{y'} and y(0)=0 s2Y(s)-sy(0)-y'(0)+6Y(s) where y(0)=0 and...

Homework Statement Let y(x)=\sumckxk (k=0 to ∞) be a power series solution of (x2-1)y''+x3y'+y=2x, y(0)=1, y'(0)=0 Note that x=0 is an ordinary point. Homework Equations y(x)=\sumckxk (k=0 to ∞) y'(x)=\sum(kckxk-1) (k=1 to ∞) y''(x)=\sum(k(k-1))ckxk-2 (k=2 to ∞) The Attempt at a Solution...

Homework Statement . Find all the solutions of the equation: ##\dfrac{\sin(y)}{x}dx+(\dfrac{y}{x}\cos(y)-\dfrac{\sin(y)}{y})dy=0## knowing that the equation admits an integrating factor ##u## of the form ##u(x,y)=h(\dfrac{x}{y})## The attempt at a solution. If I call...

Homework Statement I am trying to find the recursion relation for the coefficients of the series around x=0 for the ODE: y'''+x^2y'+xy=0 The Attempt at a Solution Therefore letting: y=\sum_{m=0}^\infty y_mx^m \therefore y'=\sum_{m=1}^\infty my_mx^{m-1} \therefore...

Homework Statement Let y(x)=\sumckxk (k=0 to ∞) be a power series solution of (x2-1)y''+x3y'+y=2x, y(0)=1, y'(0)=0 Note that x=0 is an ordinary point. Homework Equations y(x)=\sumckxk (k=0 to ∞) y'(x)=\sum(kckxk-1) (k=1 to ∞) y''(x)=\sum(k(k-1))ckxk-2 (k=2 to ∞) The Attempt at a Solution...

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...

The vector field F=<y,x> looks exactly like the the direction field for the system dY/dt = {dx/dt = y} {dy/dt = x} A few questions on this: Are the direction field of a system of ODE's the same as a vector field of calculus? In vector calc we take the line integral of a vector field...

I'm trying to decide between taking an ODE class or a PDE class next. I have already done Calculus 1,2,3 so I already know some ODEs and PDEs and linear algebra. I'm a 3rd year mathematics major with a minor in Statistics and I'm interested in applied mathematics.ODE course coverage: Ordinary...

$$\[y'sin(x)= yln(y)\] $$ Hi, I am trying to solve this one but i can't find the same result of the book: Here is my solution:

I haven't done ODEs in a while nor have a book handing. How do I tackle an equation of the form \[ 2xyy'=-x^2-y^2 \] I tried polar but that didn't seem to work.

Homework Statement $$ \left(\frac{du}{dx}\right)^2 = au^2 + bu + c $$ Homework Equations The Attempt at a Solution What method is used to solve and ODE of this form

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\sqrt{1-y^2}dx - \sqrt{1-x^2}dy=0, y(0)=\frac{\sqrt{3}}{2} rewriting the equation gives \frac{1}{\sqrt{1-x^2}}dx = \frac{1}{\sqrt{1-y^2}}dy Isn't this the integral for \sin^{-1}(x) & \sin^{-1}(y)? The back of book has y=1/2x+\frac{\sqrt{3}}{2}\sqrt{1-x^2}

Find the solution of the given initial value problem, and plot its graph. How does the solution behave as \(t\rightarrow\infty\) \(y^{(4)}-4y'''+4y''=0\) My work, which coincidentally I believe is incorrect... From the above differential equation, \(r^4-4r^3+4r^2=0\) \(r^2(r-2)^2=0\)...

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Homework Statement y''+3y'+3.25=3cost-1.5sintHomework Equations yh = e(a/2)t(Acost+Bsint) yp = Kcos(ωt)+Msin(ωt) [when r(x)=kcos(ωt) or ksin(ωt)]The Attempt at a Solution I got the homogeneous solution, which is e-1.5t(Acost+Bsint) but I am having trouble with the particular solution. I...

I have a physics problem right now, and I am so close to finishing it... The problem is to consider an undamped (no friction) forced mass-spring system. The forcing is given by $$F(t)=F_o\cos{\omega_ft}$$ The general ODE for this would be $$\ddot{x}+(0)\dot{x}+\omega_o^2x=f_o\cos{\omega_ft}$$...

Homework Statement Using method of frobenius about x=0 to solve: (1-x) y''+xy'-\frac{\alpha^2}{x^2}+=0 Homework Equations N/A The Attempt at a Solution 1. plug in series into the equation. 2. adjust the index off all the terms. 3. write the extra terms separately so that we have...

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Homework Statement Given \frac{dx}{dt} = -1.3x x_{1}(t)=e^{-1.3t} x_{2}(t)=4e^{-1.3t} Compute a solution for x(t) if x(0)=3 Homework Equations Superposition Principle and some ODE related Anyhow I refer to this http://www.youtube.com/watch?v=_ECd0Jn7y68The Attempt at a Solution First...

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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...

Should I just assume that any problems that involve integrating factor will always result in a perfect integral pair? That's probably not the right terminology but for instance if I have a differential equation which has had an integrating factor multiplied to both sides, then the left hand side...

Hi all, I have an ODE of the form \frac{d^{3}\psi}{d\xi^{3}}-A\left(\psi+\xi\frac{d\psi}{d\xi}\right)=0, where \psi=C_{1}U(\xi)+C_{2}V(\xi). Is there any transformation or inventive manipulation I can use here to obtain an ODE for \sigma=U(\xi)+V(\xi)? As this is the quantity I would...

Can anyone give me a hand with this question? I honestly have no idea how to do it? I was thinking for d(A)/dt=-d(B)/dt= -k1(A)+k-1(B) because the 2 on both sides cancels out? But this was completely wrong... Any ideas? :)

Homework Statement An object of mass ##5##kg is released from rest ##1000##m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant ##b=50##N-sec/m, determine the...

Homework Statement Find the general solution: $$\frac{dy}{dx}=(x+y+3)^{2}$$ Homework Equations The Attempt at a Solution Methods I have learned: separation of variables, integrating factor for linear equations, exact equations, and substitution. I don't even know where to begin...

For an ODE of order 2 like: X'' + λ*X = 0, how do I find the non-trivial solution in Mathematica 8? It's giving me only the trivial solution. In: ComplexExpand [DSolve[{u''[x] + \[Lambda]^2 u[x] == 0, u[0] == 0, u[a] == 0}, u[x], x]] and the out: u[x]--> 0 which is the trivial soln...

Homework Statement $$\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +{ w }^{ 2 }x={ F }_{ 0 }sinwt\quad \quad \quad \quad x(0)=0\quad \quad x'(0)=0$$ Homework Equations The Attempt at a Solution $$\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +{ w }^{ 2 }x={ F }_{ 0 }sinwt\quad \quad \quad \quad...

Homework Statement Construct a first order linear differential equation whose solutions have the required behavior as t approaches infinity. Then solve your equation and confirm that the solutions do indeed have the specified property. All solutions are asymptotic to the line y = 2 - t as t...

Homework Statement $$\frac{dy}{dx}+y=\left\{\begin{matrix}1, \ 0\leq x< 1 \\ 0, \ x\ge1 \ \ \ \ \ \ \ \end{matrix}\right.$$ Homework Equations The Attempt at a Solution $$P(x)=1$$ Integrating factor ##=e^{x}## For ##f(x)=1##: $$\frac{d}{dx}[e^{x}y]=e^{x}$$ Integrating...

Problem: xy'+2y=3x Attempt: Divide by x... y'+\frac{2y}{x}=3 I think I find the integrating factor by doing: e^{\int \frac{2}{x}dx} Not sure if that's right but if it is then the solution to the integral is just 2x. Any help is appreciated

Homework Statement Solve the initial value problem: $$sin(x)y' + ycos(x) = xsin(x), y(2)= \pi/2$$ Homework Equations The Attempt at a Solution Recognizing it as a Linear First-Order Equation:$$\frac{dy}{dx}+y\frac{cosx}{sinx}=x$$ $$P(x)=\frac{cosx}{sinx}$$ Integrating...

$$w'+2w=0\\ \frac { dw }{ dx } =-2w\\ I(x)={ e }^{ 2x }\\ \frac { dw }{ dx } { e }^{ 2x }=-2w{ e }^{ 2x }\\ \int { \frac { dw }{ dx } { e }^{ 2x } } dx=\int { -2w{ e }^{ 2x } } dx$$ Not sure what to do next.

Homework Statement Solve: ##x\frac{dy}{dx}-4y=x^{6}e^{x}## Homework Equations ##x^{-4}\frac{dy}{dx}-4x^{-5}y=xe^{x}## is equal to ##\frac{d}{dx}[x^{-4}y]=xe^x## The Attempt at a Solution The second equation above simplifies to the third (according to my textbook) but I can't figure out...

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I've been studying Walter A. Strauss' Partial Differential Equations, 2nd edition in an attempt to prepare for my upcoming class on Partial Differential Equations but this problem has me stumped. I feel like it should be fairly simple, but I just can't get it. 10. Solve ##u_{x} + u_{y} + u =...

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...

2nd Order ODE "Contradiction"? To solve a 2nd order ODE, we can follow the steps as shown below. (Image 2 is a continuation from Image 1, apologies for the size difference.) :rolleyes: The method to obtain the solution is straightforward. Let's say \frac{d^2y}{dx^2}=ky If k = -1, a...

Homework Statement A mass of 5kg stretches a spring 10cm. The mass is acted upon by an external force of 10sin(t/2) Newtons and moves in a medium that imparts a viscous force of 2N when the speed of the mass is 4cm/sec. If the mass is set in motion from its equilibrium position with an initial...

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Hey everyone I am going to be a freshman this fall (in college). I am currently having a dilemma in choosing my math class. In high school I took classes all the way up to Honors Differential Equations (ODE). In June I went to the university and signed up for Ordinary Differential Equation...

Ahoy! I'm trying to approximate f'(r) for the following equation using matched asymptotic expansions -\frac{1}{2}\epsilon ff''=\left[\left(\epsilon+2r\right)f''\right]' where \epsilon \ll 1 and with the boundary conditions f(0)=f'(0)=0, \quad f'(\infty)=1 The inner expansion which...