Ode Definition and 1000 Threads

hi, I looked up the existence and uniqueness of nth order linear ode and I grasped the idea of them, but still kind of confused why we get n numbers of general solutions.

How can i solve y" + 2y =0 with RK4 and their program fortran please I néed your helpe

Hi everyone, I am trying to find the general solution for the following ode: y'' +gy' + 10y = e2xcos(x) The solution states that the answer is y = 1/145 (5cos(x) + 2sin(x))e2x + (Acos(x) + Bsin(x))e-3x I was able to correctly find the homogeneous part of the equation as e-3x (Acos(x) +...

2nd order ODE has a form y''+p(x)y'+q(x)y=f(x)and if we assume f(x)=/=0 for every x, then y''+p(x)y'+q(x)y=/=0 so in this case we can't specify general solution of 2nd order ode?

Homework Statement $$ay''-(2x+1)y'+2y=0$$ subject to ##y(0)=1## and ##y(1)=0## where ##a## is a non-zero constant. Homework Equations Not too sure The Attempt at a Solution I know an analytic solution exists since I solved with mathematica. My thoughts were to try a series expansion, but...

Let $f$ be a solution of the following equation $y''+p(x)y=0$, $p$ is continuous on $\mathbb{R}$ such that $p(x)\leq 0$ for all $x\in\mathbb{R}$. Suppose that $f$ is defined on $[a,+\infty)$, $f(a)>0$, $f'(a)>0$, $a\in\mathbb{R}$ . Prove $f(x)>0$ for all $x\in[a,\infty)$. Any help would be...

Homework Statement Convert the following second-order differential equation into a system of first-order equations and solve y(1) and y'(1) with 4th-order Runge-kutta for h=0.5. ##y''(t)+sin(y(t))=0,\ y(0)=1,\ y'(0)=0## Homework Equations The Runge-kutta method might be applicable, but I know...

23.) y'' + 2y' + y = 4e-t; y(0) = 2, y'(0) = -1 Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as2 + bs + c) My attempt: a = 1, b = 2, c = 1 F(s) = 4 L{ e-t } = 4/(s+1) (From Laplace Transform Table) Plugging and simplifying: Y(s) = (2s2 + 5s + 7)/[(s + 1)(s2 + 2s + 1) Here is where I get...

Hello all, I would like to know how to impose a normalization condition to numerically solving an ODE. For simplicity let's consider the example \frac{dy}{dx}=y You could use different methods using an initial value, but if you consider the interval [x_0,x_1] and \int_{x_0}^{x_1} y(x)dx=1...

Hello, this is my first post here, so if I do problems, please correct me and do not be upset = ) I have one small theoretical and one greater question. small one first: Homework Statement I have a potential energy : $$W(L)= -\frac{1}{4}k_4(L_x^4+L_y^4+L_z^4)$$ How can describe my potential...

Homework Statement Use the substitution ##x=X+h## and ##y=Y+k## to transform the equation ##\frac{dy}{dx}=\frac{2x+y-3}{x-2y+1}## to the homogenous equation ##\frac{dY}{dX}=\frac{2X+Y}{X-2Y}## Find h and k and then solve the given equation Homework EquationsThe Attempt at a Solution If I...

Hi PF! I have a system of nonlinear ODE's, wherein the only constant ##C## in the ODE takes on several values depending on the geometry; thus once a geometry is defined for the ODE, ##C## is uniquely determined. Let's say I want to guess a quadratic solution to the ODE, call it ##\phi(x)##...

Hello everyone; i'd like some help in this problem : i want to solve num this differential equation { y"(t)+t*cos(y)=y } by the Taylor method second order expansion. i first have to make this a first order differential equation by taking this vector Z=[y' y] then we have Z'=[y" y'] which equal...

Are there closed curve solutions for ##\mathbf{v}(t) \in \mathbb{R}^3## satisfying this constraint? $$\mathbf{v}(t) \cdot \frac{d^2}{dt^2}\mathbf{v} = 0 $$

Hi PF! I am wondering if any of you have experience numerically solving second order ODE's? Basically, I'm trying to solve one and am trying to do it numerically in mathematica. Can anyone help? For those curious, the equation is ##y y'' + 2y'^2 +xy' = 0## where ##y## is a function of ##x##...

Hello everyone! I'm trying hard to solve numerically a system of coupled differential equations of first order, but I get this error everytime.. I can't find the reason.. maybe you can help me, I'd really apreciate that. This is the code: Jg=0.000043; Kg=0.5; Bg=0.06; Bpm=0.5; r=0.11...

$y''+\frac{1}{x}y'=\frac{2}{x^2}-4$ Hey. This is probably really simple but I'm stuck :p how do I approach this?

I'm trying to solve a 2nd order differential equation in matrix form. I'm not familiar with Matlab, and have tried solving this using tutorials on youtube. Initially, theta1 = pi/4, theta2 = 7*pi/12, theta1_d = 0, and theta2_d =0. Time interval is (0,1.2). When I try to solve this using ode45...

Homework Statement (x+1)y'' - (x-1)y' - y = 0 centred around x=1 y(1) = 2, y'(1) = 3 The Attempt at a Solution I know I am supposed to get two power series, one with a0 and one with a1 but when I am trying to figure out a pattern, I keep getting both a0 and a1 in all of my terms. So I end up...

I'm trying to solve the following equation (even if I'm not sure if it's well posed) \partial_{x} \, y(x) + a(x)\, y(x) = \delta(x) with ##\quad \lim_{x \rightarrow \pm \infty}y(x) = 0## It would be a classical first order ODE If it were not for the boundary conditions and the Dirac...

I'm a little stuck getting started on this question. y''+\tan(x)y=e^x with y(0)=1,y'(0)=0. I know the existence and uniqueness theorem for an nth order initial value problem How do I apply the theorem?

Homework Statement $$y' y + \frac{y}{x} = 1 - 2x$$ Homework Equations nothing comes to mind The Attempt at a Solution i've guessed a quadratic but that didn't work. now I'm stuck. any ideas? also, this is not homework, but a problem I am working on. Thanks!

y''-10y'+25=0 Solve the ODE with initial condition: y(0) = 0, y' (1) = 12e^5 . I keep getting y=12/5e^5x when c1=0 and c2=12/5 ... but Answer key says y=2xe^5x what am I doing wrong?

Homework Statement Is the equation (x2sinx + 4y) dx + x dy=0 linear This problem also asks me to solve it, but I don't have a problem with that part. Homework Equations An equation is linear if the function or its derivative are only raised to the first power and not multiplied by each other...

Hello! (Wave) I am looking at initial value problems for ordinary differential equations.Let $a,b, \ a<b, \ f: [a,b] \times \mathbb{R} \to \mathbb{R}$ function and $y_0 \in \mathbb{R}$.We are looking for a $y: [a,b] \to \mathbb{R}$ such that$$(1)\left\{\begin{matrix} y'(t)=f(t,y(t))\\ y(a)=y_0...

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...

I am working on a simple PDE problem on full Fourier series like this: Given this piecewise function, ##f(x) = \begin{cases} e^x, &-1 \leq x \leq 0 \\ mx + b, &0 \leq x \leq 1.\\ \end{cases}## Without computing any Fourier coefficients, find any values of ##m## and ##b##, if there is any...

Homework Statement Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose differential, dF(xy) is the left hand side of the differential equation. That is, level curves F(xy)=C are solutions to the differential...

Homework Statement [/B] A particle of mass m slides (both sideways and radially) on a smooth frictionless horizontal table. It is attached to a cord that is being pulled downwards at a prescribed constant speed v by a force T (T may be varying) Use F=ma in polar coordinates to derive an...

Homework Statement (3xy^2+4y)dx+(3x^2y+4x)dy=0Homework Equations The Attempt at a Solution So First I checked if both equations were exact. I took the derivative of 3xy^2+4y and also derivative of the other and they were both equal so the equation is exact. I took the 3xy^2+4y and integrated...

1. The problem statement, all variables and given/known da ##\frac{x^{2}}{k^{2}} + \frac{y^{2}}{\frac{k^{4}}{4}} = 1## with k != 0 this can be simplified to ##x^{2} + 4y^{2} = k^{2}## Find dy/dx implicitly, then find the new dy/dx if you want orthogonal trajectories to the ellipse. Lastly solve...

I have big problem with finite difference schemes (DS) on Matlab. I need write DS on Matlab, example: u_x=(u_(i+1,j)-u_(i-1,j))/2, we choose step is 1. On Matlab: u_x=(u( :,[2:n,n])-u( :,[1,1:n-1]))/2 And I can write u_y, u_xx, u_yy, u_xy. But now, I need to write for higher order, example...

Homework Statement Find the general solution. Homework Equations y"+y=x2sin2x The Attempt at a Solution Characteristic equation would be: m2 + 1 = 0 So,m2 = -1 Therefore, m = i or m = -i. Complementary function would be : Asinx+Bcosx where,A and B are constants respectively. If I write...

Homework Statement {Prob #27, Section 2.1 "EDE" (Boyce/Prima, 10thEd), pp. 40} "Consider the initial value problem [and] find the coordinates for the first local maximum point of the solution, t>0." Homework Equations y' + (1/2)y = 2cost y(0) = -1 The Attempt at a Solution I...

Hello again, I've got another trouble with a new differential equation: (x^2+2)y'''-(x^2+2x+2)y''+2(x+1)y'-2y=0 I did a try using matrices(file is attached), however the system to be solved is hard to compute. Do you have any idea to help me solve this out?

Hi, I am trying to solve the following ODE for my maths project: ## y'' = \frac{\alpha}{2}y^3 - \frac{3}{2}y^2 + y - \frac{3}{x} y'## under the following boundary conditions: ## y'(0) = 0 ## ## y(x) \rightarrow y \_ \equiv 0\ \text{as}\ x \rightarrow \infty ## As a first step, I converted...

While fiddling around with some very simple linear ODEs, I "discovered" a formula that gives a solution to ODEs of the form: ##y'+y=ax^n ##. here it is: i'm sure that this was discovered before, but i was just wondering if it had any official name or something.

Is the solution of differential equation be unique always?

why not the 2nd order linear homogeneous ODEs have three Linearly independent solutions or more? I know for the characteristic equation, we can only find 2 answers but.. just wondering if that is the only case to solve the question and if it is, then why it has to be. so my question is,1. 2nd...

Homework Statement Solve the following: [/B] y'' = c2 / (x2 + c1*x) * y c1, c2 are constants, x is variableHomework Equations As above The Attempt at a Solution I have used the method of Frobenius and regular power series and obtained an infinite series on top of an infinite series, which is...

I've decided to finish off this stage of my GR problem by finding an interval over which the acceleration of the object is "roughly" constant. I don't need help with the Math per se, but I would like your opinion on the method I am proposing. The Math is sufficiently ugly that I'd like some...

Homework Statement I have a differential equation that I need to solve numerically by writing a program. x0, y0, x_dot0, y_dot0, α are all given Hello, I have the following differential equation: http://puu.sh/d78KC/107bd6c71f.png I want to rewrite it so I can solve it numerically by writing...

if I consider a circuit consisting of a capacitor, an inductor and a resistor and using kirchhoffs voltage rule for the circuit i come up with the following L(Q''(t)) + R(Q'(t)) + (Q(t))/C = 0 I solve for the roots using a characteristic equation of the form LM2 +MR +(1/C) = 0 solving this for...

Hello, can someone advise me how to solve numerically ODE which consist of function with "critical point" (Im not sure if it is good definition)? I mean for example this one: y'(x)=\frac{\sin{x}}{x}, where in x=0 has function a "problem". I know that limit ->1 but in numerical solutions it...

Homework Statement I'm taking an online introductory chem course, and while explaing the failure of classical mechanics to describe electron behavior, the teacher brought up the following ode which is based on Newton's second law and coulombs law: -e^2/4(pi)(epsilon-nuaght)r^2=m(d^2r/dt^2)...

Homework Statement 8t^2 * y'' + (y')^3 = 8ty' , t > 0 Homework EquationsThe Attempt at a Solution I tried using the substitution v = y' to get: 8t^2 * v' + v^3 = 8tv I rewrote it in the form 8t^2 * dv/dt + v^3 = 8tv, and then moved the v^3 to the other side to get 8t^2 * dv/dt = 8tv - v^3...

Solve the linear equation: x\frac{dy}{dx}-y=x^2sinx rewrite \frac{dy}{dx}-\frac{y}{x}=\frac{x^2sinx}{x}=xsinx P(x)=\frac{-1}{x} So e^ { \int \frac{-1}{x} dx }=-1<=this is where I went wrong \frac{d}{dx}[-y]=-xsinx \int -x sin(x)=xcosx-sinx +C but the answer key gives y=cx-xcosx

Homework Statement Find the general solution: y'-3y=(y^2) Homework EquationsThe Attempt at a Solution divide both sides by y^2 y'(y^-2) -3(y^-1) = 1 we know v=y^(n-1) v=y^-1 v'=d/dx(y^-1) v'=-(y^-2) y' plug it back into y'(y^-2) -3(y^-1) = 1 -v'-3v=1 this is where I think I am making a...

Hello , I tried to solve this coupled ODE but with no success Does anyone know if there is an analytical solution to this equation? my problem is with the first & the second equations the term g*f is the my biggest problem i think once i have the solution for g - the solution for h is...

Homework Statement The suspension system of a car traveling on a bumpy road has a stiffness of ##k = 5\times 10^6## N/m and the effective mass of the car on the suspension is ##m = 750## kg. The road bumps can be considered to be periodic half sine waves with period ##\tau##. Determine the...