Second order Definition and 570 Threads

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.

Consider this sequence: 1, 2, 3, 4, 5, ... We can calculate the n'th term of the sequence by the function t(n) = n. We could define s(n), the sum to n terms, recursively as s(1) = 1 and s(n) = n + s(n-1). The time bound of this procedure is O(n), but it isn't efficient because we can...

Hello, I am having trouble understanding how to solve second order nonhomogeneous linear differential equations. I know how to solve second order homogeneous linear differential equations. But I am not following in the lecture and in the text the method of variation of parameters to solve...