Second order Definition and 602 Threads

Second order diff.eq. help?? well i am trying to find a solution to this diff. eq, but i get stuck somewhere. \ 4x^{2}y''+y=0 I first took this substitution y'=p, y"=p' so the diff. eq becomes of this form \ 4x^{2}p'+p=0 i think this can be done with the separable of variables...

Homework Statement solve y"+y=xsin(x) , initial conditions y(0)=0, y'(0)=1 Homework Equations The Attempt at a Solution I know that when right hand side equals something like sin(x), then the particular integral is xc1sin(x)+xc2cos(x). I am unsure what the particular integral...

Homework Statement Solve the reducible 2ODE. Assume x, y and/or y' positive where helpful. y^3 * y'' = 1 The Attempt at a Solution Well, I tried what I normally would do for x being missing. p = (dy/dx); y'' = p'p = (dp/dy)(dy/dx) So y^3 p'p = 1 p(dp/dy) = y^(-3)...

Solve the initial value problem y''+3y'+2y = 3e^{2t}+1 with initial values y(0) = 1, y'(0) = 1. I am unsure if I am going about the solution correctly. 1.) Find the characteristic equation. r^{2}+3r+2=0 \Rightarrow (r + 1)(r + 2) = 0 Therefore, y = c1•e^{-t}+c2•e^{-2t} 2.) Use method of...

Homework Statement Consider the second order differential equation y'' - 4y' + 4y = f(x) Find a particular solution if f(x) = 25cos(x) Homework Equations I believe for this type of question I should let y = Asin(x) + B cos(x) Hence y' = Acos(x) - Bsin(x) and y'' = -Asin(x) -...

Quadratic Polynomial can't satisfy second order linear differential equation with constant coefficients... WHY? and if possible, how would I show this? Does it have to do with independence?

I am sure most of you are familiar with the equation: m(x)''+c(x)'+k(x) = 0. Then, we create an auxillary equation that looks like this: mr^2+cr+k = 0. And, then we find the roots of this auxillary equation, calling them r1 and r2. And, if the roots are r1,r2>0 we consider the system to be...

Solve by direct substitution taht the function \phi(t) = Asin(wt) + Bcos(wt) is a solution of the second order differential equation \ddot{\phi} = -w^{2}\phi. ( Since this solution involves two arbitrary constants - the coeffecients of the sine and consine functions - it is in fact the general...

I need to solve the equation \frac{d^{2}}{dx^{2}}\Psi + \frac{2}{x}\frac{d}{dx}\Psi = \lambda\Psi Can anyone help me get a start on this problem? I've been guessing at a few solutions with no results... I'm not asking anyone to solve the problem... just a few hints on starting... maybe...

Homework Statement Have to use the product rule twice. \frac{d}{dx}=x^4e^xsin(x)[/itex] I got about as far as the first use of the product rule then stalled when I had to use it again. got this:- (1+x^2)sin(x)+(x^4e^x)sin(x) but not this:- (4x^3e^x+x^4e^x)sin(x)+x^4e^xcos(x) Problem is...

Hello everyone The following two differential equations appear on page 93 of George Simmons' book on Differential Equations. While I have been able to solve them, I have some questions. [Not HW] I. (x^2-1)y'' - 2xy' + 2y = (x^2-1)^2 II. (x^2 + x)y'' + (2-x^2)y' - (2+x)y = x(x+1)^2 How I...

Homework Statement In the circuit below, determine v_o(t) for t > 0. Let V_{IN}\,=\,u(t)\,V, R_!\,=\,R_2\,=\,10\,k\Omega, C_1\,=\,C_2\,=\,100\,\muF. http://img249.imageshack.us/img249/3840/problem867cg5.jpg Homework Equations i_c\,=\,C\,\frac{dv_c}{dt} The Attempt at a...

Homework Statement Obtain i_1 and i_2 for t > 0 in the circuit below. http://img258.imageshack.us/img258/7765/problem60as1.jpg Homework Equations V_L\,=\,\frac{di_L}{dt} The Attempt at a Solution To get initial conditions, I made a second circuit diagram for t < 0...

Homework Statement http://img396.imageshack.us/img396/2781/chapter8problem55oy6.jpg For the circuit above, find v(t) for t\,>\,0. Assume that v\left(0^+\right)\,=\,4\,V and i\left(0^+\right)\,=\,2\,A. Homework Equations i_c\,=\,C\,\frac{d\,v_c}{dt} The Attempt at a Solution I made a new...

Homework Statement This is the result of a problem from my Quantum class, but I figure it would be best to ask in here as my question is purely a question of how to solve a certain differential equation. the equation is of the form 0=Y''-i*a*Y' + b*Y where Y is a function of t So the...

In general how do we deal with linear second order differential equations with variable coeffecients?

Here's the problem: x^2y''-3xy'-12y=0 with initial conditions y(1)=0 and y'(1)=7 I'm supposed to solve for y in the form y=c1y1+c2y2 y1 = x^6 by inspection Now to solve for y2 y2=y1v v can be solved for by the equation y1v''+(2y1'+py1)v'=0 where p is the function in front...

Crap, nevermind, I left b^2 out of the quadratic formula, thanks anyways. Here's the question: Find y as a function of t from the diff eq: y''+6y'+25y=0 with the initial conditions y(0)=8 and y'(0)=8 I used the form r^2+6r+25=0 to solve for r and through the quadratic equation got r =...

I am having a problem coding a Matlab code that solves a second ODE equation which I give below: x^3*(1-2*x*M)d^2J(x)/dx^2+2*(2*x^2+i*nu*x-7*x^3*M)*dJ(x)/dx -2*(2*x+8*M*x^2+i*nu)*J(x)=0. where M = 1 (Mass of a black hole), nu = 0.74734+0.17792*i, J is a function of x, i represents a...

I am having a problem coding a Matlab code that solves a second ODE equation which I give below: x^3*(1-2*x*M)d^2J(x)/dx^2+2*(2*x^2+i*nu*x-7*x^3*M)*dJ(x)/dx -2*(2*x+8*M*x^2+i*nu)*J(x)=0. where M = 1 (Mass of a black hole), nu = 0.74734+0.17792*i, J is a function of x, i represents a complex...

d2y/dx2+k*dy/dx = du/dx+u anyone got a hint how to use ODE to sovle this inhomogenous equation? Thanks a lot

Second Order Equations! Can Anybody help me?? Greatly appreciated! Homework Statement Interpret x(t) as the position of a mass on a spring at time t where x(t) satisfies x'' + 4x' + 3x = 0. Suppose the mass is pulled out, stretching the spring one unit from its equilibrium position, and...

Homework Statement Homework Equations HalfLife = 1 / k*[A]i where k is the rate constant and [A]i is the initial concentration of a reactant A. The Attempt at a Solution I don't have enough information to attempt this problem. I don't know what to do with the partial pressure...

I need help solving this equation y''+y'+y= sinx I know it looks simple but It seems to be getting sticky! I have been trying to solve it using variation of perimeters,maybe there is a quicker way? If anyone can help please...:bugeye:

I need some help on finding the general solution. I can find the complimentary solution, I'm having trouble finding the particular solution. Can anyone give me any tips. y"+9y=t^2e^(3t)+6 y"-2y'-3y=-3te^-t y"+2y'=3+4sin(2t)

I am having real trouble with this second order differential The substitution is given and i just can't seem to use it What am i missing here? x \frac{d^2 y} {dx^2} -2 \frac{dy} {dx} + x = 0, \frac{dy} {dx} = v All help welcome

Hi All, I have a differntial equation that I came up with on a little engineering problem posted here https://www.physicsforums.com/showthread.php?t=129247 that I can't solve. It is d^2R/dt^2=W^2*R where R is radial position and W is angular velocity and t is time. I think it is an autonomous...

I was wondering what the best method is to solve two second order differential equations that are coupled. I need to solve it by hand and write my own code so I cannot use built in functions in matlab, etc. At time (0), displacement and velocity are 0 with an initial acceleration which is...

A simple question i think although i can't find in any books What do u when u are solving a second order linear hoemoeneous differential equation with frobenius and there is no shift. (X^2)(y^{''}) (-6y)=0 it should be normal minus -6y I only know what to do if there...

Are there any analytical solutions to: ay''+bx^2y+cxy+dy=0 where a,b,c,d are constants and y(x) If so how would you go about it? Is there a website that teaches you how to solve these?

I'm using the method of undetermined coefficients here, but I'm either not making the correct ansatz or I'm just confused on the method. The problem is 2y'' + 3y' + y = t^2. I gussed Y = At^2. Is this correct? It doesn't solve the differential equation, which is the only check I know...

I just came across this one, was going really well until i came across this one. (d^2y/dx^2) + (dy/dx) = e^(-x) m^2 + m = 0 m = -1 and m = 0 Now i get the particular integral Try y = ke^(-x) (dy/dx) = -ke^(-k) (d^2y/dx^2) = ke^(-x) ke^(-x) - ke^(-x) = e^(-x) I get stuck here...

Hi , I am stuck with the following problem: Find a second order linear homogeneous equation having the pair as a fundamental set of solutions: y1(x)=x , y2(x)=x*ln(x). My problem here is that I don't have the exponential form for the proposed solutions. Thank you for your help B.

Regarding: (a+bx+cx^2)y^{''}+(f+gx+hx^2)y^{'}+(j+kx+mx^2)y=0 Does anyone here know if it's been "completely" characterized in terms of the geometry of the three parabolas which make up it's coefficients? For example, if I'm given plots of the parabolas, can any information at all be...

So, the average rate for a reaction of type A --> product is given by \text{rate} = -\frac{\Delta A}{\Delta t}. Also, \text{rate} = k \cdot \text{A}. The instantaneous rate for a reaction of that type is \lim_{\Delta t\rightarrow\0} -\frac{\Delta A}{\Delta t} = -\frac{dA}{dt}. Setting the...

Consider the second order linear equation z" + c(t)z = 0 Where c(t) is a continuous real-valued function of a real variable. (a) Show that every (nontrivial) solution of this equation is non-oscillatory if c(t) < (1 - epsilon)/(4t^2) for t>=1, where epsilon > 0 is a real number...

hi, I have a question showing the 'particle in a box' example of the 1-d schrodinger equation, and given the initial conditions (walls of infinite potential, zero potential inside the box) the time-independent equation reduces to d^2y/dx^2 = -k^2y, where k is a constant - my text just gives...

hi guys need some help on diff eqn, I've done the workingout and answers but not sure if they are right mind if someone can check them for me thanks Find the general solution of the differential equation dy/dx - 2y = e^(5x) i found I(x) = e^ integral (-2 dx) = e^(-2x) as I(x) =...

The following equation was derived from a RLC circuit: \frac{d^2}{dt^2} (V(t)) + 6 \frac{d}{dt} (V(t)) + 5V(t) = 40 Setting up the equation: s^2 +6s + 5 = 0 yields s = -1 and s = -5 Giving me the general equation: V(t) = k_{1}e^{-t} + k_{2}e^{-5t} But the general equation...

Assume the next differential LINEAR second order equation: w''+\frac{4}{x}w'+\frac{4}{x^4}w=0 So I thought: OK, I need two independent solutions w_1 and w_2, because the space of solutions is of dimension two. Then the professor gave us a solution: w=sen(2/x)-(2/x)cos(2/x) and I...

First and Second order phase transitions At a first order phase transition as energy is added the system will absorb it, it involves latent heat I s'pose, water to steam, gel to glassy etc.. but what happens in a scond order phase transition? and in both cases how is the specific heat capacity...

Hello, Please help me out here as I self study fluid mechanics. I ran into what they are calling a second order tensor quantity, which seems to be fancy words for a 3x3 matrix of sigmas and rhos, for shear and normal stress. They have a picture of a cube, with all the positive stresses...

I have a 2nd order homogeneous non-const. coefficients linear DE, and don't remember how we used to solve it or even if we did at all, looked through the book, but it only covers a case of Cauchy-Euler. The original question actually goes like this: verify that y(x) = sin (x2) is in the...

Hello, not sure if it's a typo in the book but I can't work this out: y'' + y(x^2 + e^x) = 0; It's second order but both dependent and independent variables are present, and i am stuck. You don't have to solve it for me entirely, a hint would be great. Thanks in advance.

I need to solve the following second order nonlinear differential equation: z''(b) * [6(1 - f)z(b) + (1+f)b z'(b)] = (15 - 9 f)[z'(b)]^2 + [2(1 - f) z(b) z'(b)] / b + [4 f z'(b)^(5/2)] / b^(1/2) where f is a constant between [0,1]. initial conditions are z(0)=0 and z'(0)=0 I...

Hello. First post here. I'm trying to write a program (from scratch) to simulate a double inverted pendulum (a cart with 2 pendulums one on top of the other). The system is modeled with a system of 3 second order ODE's, which I need to solve numerically using Runge Kutta. I know how to solve...

forever! I missed a day of notes, I know for the second order Y(n+1) =(approx.) Y(n)+K2, and I have the algorithm for finding k1 and then k2, how does this differ from the 4th order?

Suppose we have y'' = f(t, y); y(a) = y0; y'(a) = y0' Note all derivatives are with respect to t. Let u = y', then u' = y'' 1. u' = f(t, y), u(a) = y'(a) 2. y' = u, y(a) = y0 Question 1: For y' = u, should I think of this as dy/du = u? Otherwise, I don't see how to solve 2 because...

Ok, this one is really sticking me up: y'' - 2y' + 2y = e^{t}cos(t) I solved the homogenous version and got roots 1 +/- i and put these into get the equation y_h = c_1e^tcos(t) + c_1e^tsin(t) And I found that the root for e^tcos(t) should be (D- (1 +/- i) But I'm completely stuck...

How would I go about finding a solution to this differential equation? r\ddot\theta-g\sin\theta=0 Where r and g are constants.