Ode Definition and 1000 Threads

y'' + 2y' + 3y = 0, y(0) = 0, y'(0) = 1 Char. Eqtn. is $p^2 + 2p + 3 = 0, \therefore p = 1 \pm i \sqrt{2}$ Solutions of the form $p=r \pm iq$ are $y = e^{rx} \left( C_1 Cos qx + c_2 Sin qx \right) $ $\therefore y = e^{x} \left( C_1 Cos qx + c_2 Sin qx \right) , q= \sqrt2$ Now $y' =...

Hi all i want to write a MATLAB code by runge kutta solution for hiemenz equation. F''' + FF'' + 1 - F'^2 = 0 BCs F(0)=F'(0)=0 and F'(inf)=1 I have programmed for RK Fehlberg, RK4 and RK5 method but the results of these three methods are not matching with actual values. In the cod I defined...

Hi - I have y''+9y=0 which is a constant coefficients ODE, the CE is then $r^2+9=0$ and I get a general solution $ y=C_1e^{3ix}+C_2e^{-3ix} $ But I have seem these solutions written as ACos3x+BSin3x. If I use Euler on my solution, I get $ C_1(Cos3x + iSin3x) +C_2(Cos3x-iSin3x) $ ... Are they...

Greetings, what is the intended audience of Arnold's ODE book? I have completed a computational style ODE course, 3 semesters of Calculus from Stewart's book and a Linear Algebra Course. Will I need higher mathematics in order to study Arnold's book on ODE?

Hi, is there a way to add a user defined convergence criteria to an ode solver so that the solution is stopped?

Hi everyone! I'm thinking of buying Arnold's book of ODE, but looking for it on the internet I have found two publishers which have this book printed: MIT Press and Springer. The main question is: which edition is better? Both editions haven't the same quantity of pages, maybe because of...

if we assume the condition immediately after switch is closed (t=0+), *Capacitor voltage cannot jump. *Inductor current cannot jump. dv(0+)/dt=i_c(0+)/c di(0+)/dt=v_l(0+)/L which means we can find the initial condition of the post-zero system algebraically. However, it contradcits to the...

I have an equation of motion given by $$f(z(t),t) = \frac{d^2z}{dt^2} + A\frac{dz}{dt} + B $$ where $$f(z(t),t) = [(\frac{C}{z^2+C^2})^2-(\frac{D}{z^2+D^2})^4]^2(1+cos(wt))$$ and ##A,B,C,D,## and ##w## are constants Is it possible to solve this for ##z(t)##? I have been solving it numerically...

It's been too long guys. I've given this ODE lots of thought and still no cigar. Homework Statement We are given the following ODE: $$ (x-a)y''-xy'+a^2y = a(x-1)^2e^x $$ and knowing that y=e^x is a solution to the homogenous equation, find the possible values of a. Next part: Using the...

I have this question due soon and I have no idea how to do it. Please help me get started on it Solve in powers of x: (1-x^2)y''-2xy'+42y=0

Homework Statement By making the transformation u= x^αy where α is a constant to be found, find the general solution of[/B] y'' + (2/x)y' + 9y=0The Attempt at a Solution I've worked out y,y',y'' and subbed them into get x^-au'' + x^a-1(2-2a)u' + x^-a-2(x^2-a(a-1))u =0...

If i have 3y" - 2y' -y = 14 + e2x+8x And i want to find the general solution. Obviously first i obtain the characteristic eqn, yc, by making it into a homogeneous eqn. Then i can get yp BUT Am i able to get yp for the e2x and the 14 + 8x separately, then add them together for yp?Thanks

I would like to solve the steady-state one dimensional heat equation for a two piece material system. The thermal conductivity in each segment is a linear function of temperature, where ##\kappa_1=a_1T+b_1## for material 1 and ##\kappa_2=a_2T+b_2## for material 2. ##a_1, a_2, b_1, and \;b_2##...

Homework Statement Given the differential equation (\sin x)y'' + xy' + (x - \frac{1}{2})y = 0 a) Determine all the regular singular points of the equation b) Determine the indicial equation corresponding to each regular point c) Determine the form of the two linearly independent solutions...

Hello, I'm recently trying to code a solver for a system of differential equations u'(t) = F(t,u), using a Runge Kutta 4 method with an adaptative stepsize. For this, I'm using the 'step doubling' method, which is the following : suppose that we now the solution u(i) at time t(i). Then, the...

Homework Statement Y''-((Y')^2)+(C1*exp(Y))=C2 C1 and C2 are constants. exp = e Homework Equations No clue how to start this The Attempt at a Solution Y'=A=dY/dt Y=At+C3 (not sure) A'-(A^2)+C1exp(At+C3)-C2=0 A'-(A^2)+C1exp(C3)exp(At)=0 let C=C1*exp(C3) A'-(A^2)+Cexp(At)=0

dx/dt = x-y^2 dy/dt= x^2 -xy -2x For each critical point, find the approximate linear OD system that is valid in a small neighborhood of it. I found the critical points which are (0,0),(4,2),(4,-2) but have no idea how to do the above question! please help!

Hi everyone I have a system of ODE as follows x1_dot=f1(t)-ax1 x2_dot=f2(t)-ax2 x3_dot=f3(t)-ax3 f1,2,3(t) are unknown nonlinear functions of time, a is constant and unknown, x1,2,3 and their derivatives are given. How can I estimate the parameter a from the given information? Thanks

Homework Statement Find the amount in a savings account after one year if the initial balance in the account was $1000, the interest is paid continuously into the account at a normal rate of 10% per annum (compounded continuously), and the account is being continuously depleted at the rate of...

Homework Statement (Reduction of order) The function y1 = x-1/2cosx is one solution to the differential equation x2y" + xy' + (x2 - 1/4) = 0. Use the method of reduction of order to find another linearly independent solution. The Attempt at a Solution I divided x2 to both sides to get the...

Hi there, in my notes for Heun's method for solving an ODE, I have y(new) = y(old) + 0.5(k1 + k2)Δh And k1 is supposed to be f(y(old)) while k2 is f(y(old) + q11k1Δh) and q11 is 1 So if for example I have a simple differential equation like du/dt = au It would be du/dt = 0.5(k1 + k2) du/dt...

Im trying to implement the implicit Euler method in high-performance software for micromagnetic simulations, where I'm restricted to using the driving function of the ODE (Landau-Lifshitz equation) and the previous solution points. This obviously not a problem for an explicit method, since we...

Homework Statement Let ##f(t)= \begin{cases} \sin t , \; \; 0 \le t < \pi \\ 0 , \; \; \; \; \; \text{else.} \end{cases}## Use Laplace transform to solve the initial value problem ##x'(t)+x(t)=f(t), \; \; \; x(0)=0.## Homework Equations Some useful Laplace transforms...

Homework Statement Give an example of a system of differential equations for which ##(t,1)## is a solution. Homework Equations Nothing comes to mind. The Attempt at a Solution I thought to initial pose the system as an eigenvalue problem ##\vec{x}' = A \vec{x}##. However, ##(t,1)## is...

Homework Statement I've been stuck on this problem for three days now, and I have no clue how to solve it. Construct a linear differential equation of order 2, for which { y_1(x) = sin(x), y_2(x) = xsin(x)} is a set of fundamental solutions on I = (0,\pi) . Homework Equations Wronskian for...

Homework Statement Okay the problem is of a free swinging pendulum with dampening which is modeled using the following equation: Damping coefficient: c=1 s−1 Mass: m=1 kg Gravity: g=9.81 ms−1 Link length: l=0.5 m We know θ(0)=90° and θ′(0)=0, solve this equation from t = 0 to t = 10...

I have the following system of differential equations, for the functions ##A(r)## and ##B(r)##: ##A'-\frac{m}{r}A=(\epsilon+1)B## and ##-B' -\frac{m+1}{r}B=(\epsilon-1)A## ##m## and ##\epsilon## are constants, with ##\epsilon<1##. The functions ##A## and ##B## are the two components of a...

If an ODE of 2nd order like this A y''(x) + B y'(x) + C y(x) = 0 has how physical/electrical interpretation a RLC circuit, so, how is the electrical interpretation of a system of ODE of 1nd and 2nd order? \begin{bmatrix} \frac{d x}{dt}\\ \frac{d y}{dt} \end{bmatrix} = \begin{bmatrix}...

Look this schematic picture: S means source and can be a current source or a voltage source. C_1, C_2 and C_3 are linear components, can be resistor, capacitor and inductor. In the everycircuit, I tried set up all possible combination and the everycircuit denied some combinations, but...

1) Given $\mathcal{L}u=0$ and $ g\mathcal{L}u$ is self-adjoint, show that for the adjoint operator $ \bar {\mathcal{L}}, \bar{\mathcal{L}}(gu)=0$ Is it enough to say that if self-adjoint, then $ \mathcal{L}= \bar {\mathcal{L}} $. I assume g represents a function of x (so no inner products with...

Hi, my textbook claims $ <u|\mathcal{L}v> =\int_{a}^{b}u^*\mathcal{L}v \,dx = \int_{a}^{b} u(p_0u''+p_1u'+p2u) \,dx$, u,v matrices or functions My only query is why $u^*$, and where did the * get to in the 2nd integral? I am used to $ <f|g>=\int_{a}^{b}f(x)g(x) \,dx $ ...

..when it is released from rest with velocity (v0, 0) I can get 1.6.5 but I can't get this:

Homework Statement Suppose an RC series circuit has a variable resistor. If the resistance at time t is given by by R = a + bt, where a and b are known positive constants then the charge q(t) on the capacitor satisfies (a+bt) q' + (1/C)q = V where V is some constant. Also q(0) = q_0 Find q(t)...

Homework Statement My question is regarding part (e), I just gave all the questions for reference. Homework EquationsThe Attempt at a Solution These are the coupled equations I should solve (from part d) My issue is using ode45 to get ##C_{A}(t)##, ##C_{P}(t)##, and ##T(t)##. Here is my...

I have a question regarding the solutions to linear-ordinary differential equations. I had originally learned that the solutions to such differential equations consist of a homogenous solution and particular solution. The homogenous response is due to initial conditions while the particular...

Hi, I need to solve 3 coupled first order ODE's using NDSolve (numerical solution). This is the code I have used ; NDSolve[{u'[t] == ((1 - (u[t]/t^2))/(-3 - (u[t]/t^2) - (v[t]/t^2))), v'[t] == (((u[t]/t^2) - (v[t]/t^2))/(-3 - (u[t]/t^2) - (v[t]/t^2))), w'[t] == (v[t])/(-3 t^2 - (u[t]) -...

Homework Statement dy/dx + 2sin2pix = 0 -------Answer: y = 1/pi cos2pix + c Homework EquationsThe Attempt at a Solution I made several attempts but no success to the correct answer. The first step I made was subtracting 2sin2pix to both sides. I then used integration by parts, and this is...

The ODE is $ \d{}{x}[(1-x^2)\d{u}{x}]+\alpha u + \beta x^2u = 0 $. I know of Legendre's ODE, and Bessles and a few others - does this one also have a name?

Given standard ODE $ y'' + P(x)y' + Q(x)y=0 $, use wronskian to show it cannot have 3 independent sltns. Assume a 3rd solution and show W vanishes for all x. so 1st row of W = {$ {y}_{1}, {y}_{2},{y}_{3} $}, 2nd row is 1st derivatives, 3rd row is 2nd derivatives. I can find the determinate...

Homework Statement I have been trying to solve the following nonlinear ordinary differential equation: ##-\Phi''-\frac{3}{r}\Phi'+\Phi-\frac{3}{2}\Phi^{2}+\frac{\alpha}{2}\Phi^{3}=0## with boundary conditions ##\Phi'(0)=0,\Phi(\infty)=0.##Homework Equations My solution is supposed to...

Frustratingly although I can solve the ODE, I am getting a different answer to the book. Now going in circles so would appreciate a fresh pair of eyes. The ODE (for a boat coasting with resistance proportional to $V^n$) starts as $ m\frac{dV}{dt} =-kV^n $ Find V(t) and x(t), V(0) = $V_0$ I...

I need to find a trapping region for the next nonlinear ODE system $u'=-u+v*u^2$ $v'=b-v*u^2$ for $b>0$. What theory i need to use or which code in Mathematica o Matlab could help me to find the optimal trapping region.

Two questions: First: If is possible to reduce the order of an ODE increasing the number of equations, so, is possible do the inverse patch? In other words, is possible reduce the number of equations of a system of ODE increasing the order? Second: This technique of reducing and increasing of...

Someone can explain me how to get the general solution for this system of ODE of second order with constant coeficients: \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22}\\ \end{bmatrix} \begin{bmatrix} \frac{d^2x}{dt^2}\\ \frac{d^2y}{dt^2}\\ \end{bmatrix} + \begin{bmatrix} b_{11} &...

During the summer, I plan on learning differential equations (ODE's and PDE's) from bottom to top, but I am unable to choose books due to a great variety present. Can you suggest books for me to read in the following order (you can add as many books in each section if you like);Ordinary...

Hello everyone! I am currently playing with an old analog computer, which could solve time-dependent ODE/PDEs pretty fast, without time-stepping. But the problem with analog computer's solutions is that they are not very accurate. I am very curious that is there any numerical method/solver which...

Homework Statement A weight of 8 pounds extends a spring 2 feet. It's assumed that the damping force that acts on the system is equal (number-wise) to alpha times the speed of the weight. Determine the value of alpha > zero so x(t) is critically damped. Determine x(t) if the weight is liberated...

if we do picard's iteration of nth order linear ODE in the vector form, we can show that nth order linear ODE's solution exists. (5) (17) example) (21) (22) (http://ghebook.blogspot.ca/2011/10/differential-equation.html)I found that without n number of initial conditions, the solution...

Hi PF! Can any of you help me reduce this ODE to find a solution? $$y y''+2y'^2+xy'+\frac{1}{2}y = 0 \implies \\ (y y')'+y'^2+xy'+\frac{1}{2}y = 0 \implies\\ (yy')'+(xy)'+y'^2-\frac{1}{2}y=0$$ but here I am stopped. Am I even going the correct route? I know I can re-write this equation as...

Homework Statement Solve dy/dx = y/x + tan(y/x) Homework EquationsThe Attempt at a Solution Not separable, as far as I can tell. It's not homogeneous, since for the tan term f(λx,λy) = tan(λy/λx) = tan(y/x) ≠ λtan(y/x). It's also not of the form dy/dx + P(x)y = Q(x), because I don't think Q(x)...