2nd order Definition and 494 Threads

Hi, have this strange 2nd order ODE in one of my tutorials that I am struggling to start. I am not used to dealing with derivatives of both x and y as well as a function involving t. I was wondering if anyone may be able to point me to the starting line. I am trying to convert them into 1st...

what's the method to solve a diff. equation as follows: d^2(psi)/d(x^2) - (k^2)*(psi) = 0

I'm working on a complex analysis problem from Arfken. Integrate[ (cos(b*x)-cos(a*x))/(x^2), {x, -Infinity, Infinity}] and show that it is equal to Pi*(a-b) Attempt: I first look at a related problem (or one that I think is related). => f(x) = sin(x)/x => f(z) = sin(z)/z...

Homework Statement A curved mirror of equation y=y(x) has that property that whenever a ray of light emanates from the origin it reflects parallel to the x-axis. Find the equation of the mirror Don't even know how to get started on this, Don't need a solution just need some starting hints...

Homework Statement y1 = x2 and y2 = x3 are two different solutions of x2y'' - 4xy' + 6y = 0, both satisfying the initial conditions y(0) = 0 = y'(0). Explain why these facts don't contradict Theorem 2 (with respect to the guaranteed uniqueness). Homework Equations The Attempt at a...

Homework Statement Find the particular solution of the linear, homogeneous, 2nd order differential equation: y'' - 2y' + 2y = 0, given the solutions y1 = (e^x)*(cos x), y2 = (e^x)*(sin x), y(0) = 0, y'(0) = 5. Homework Equations The Attempt at a Solution How do I begin? I'd really...

Homework Statement Verify that y1 = (e^x) * (cos x) solves the linear, homogeneous, 2nd order differential equation y'' - 2y' + 2y = 0 Homework Equations The Attempt at a Solution So I used the product rule but just kept going in circles with the cos x. I remember there's a way to...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

Homework Statement \left(\frac{dy}{dx}\right)^2 - 4x\frac{dy}{dx} + 6y = 0 Homework Equations A common approach we have used for similar problems has been to let P = dy/dxThe Attempt at a Solution Doing so we have: P^2 - 4xP +6y = 0 \Rightarrow 6y = 4P(x - P) Differentiating gives: 6P...

Homework Statement Find a value of the constant r such that both e^rt and te^rt are solutions to the ODE ay''+by'+cy=0 Homework Equations The Attempt at a Solution can anyone guide me with this question please. I am not sure where to start. I know that e^rt is always a solution...

Homework Statement y'' -2y' +5y =0 , y(0)=1, y'(0)=1 you get a complex root conjugate. Homework Equations y=e^(rt) y'=re^(rt) y''=r^2 * e^(rt) The Attempt at a Solution I have in my notes sin(omega*t)e^(sigma *t), cos(omega *t)e^(sigma). I don't think i took down the notes...

i would like to programing in MATLAB with runge kutta 4 with 2nd order the variables (x with y and Q) where x distance , y hight of water and Q discharge from the following tow equation dydx = (s0-(((Q0^2*n^2)/(B^2.*y^(10/3))*(1+2.*y/B)^(4/3))+dQdx))/(1-Q0^2/(g*B^2*y.^3)); dQdx =...

Hi, I've spent days trying to solve some equations in a paper (referenced below) that describes it as a "straightforward, albeit lengthy integration," but I can't work out the "straightforward" bit. The notation is also odd, which doesn't seem to help my problem. Perhaps someone could help...

Hello everybody, could you please direct me how to solve this nonlinear differential equation analytically, so by mathematica or matlab? I really need to solve it for my research project, so please help me du/dx=d/dx[a*u^(-1/2)*du/dx]-n*u^(3/2)*(u-c)/b boundry conditions are: u(0)=b+c...

Hi Guys, I know how to find the solution to a 2nd order homogeneous with constant coefficients but how do you solve one with a non constant ie x^2y''+2xy' ... etc = 0 Is there a general solution formula for these types of problems? My book seems to jump from 2nd order...

What does "to 2nd order" mean? http://www.mathpages.com/rr/s2-11/2-11.htm I thought "to second order" meant an approximation consisting of the initial terms of the Taylor series up to and including the second derivative term. For example, it seems to be used that way in the Wikipedia...

Homework Statement This was an example the teacher gave us to do in class. Unfortunately, I was a little behind on the notes so was not able to copy down the steps to solving this one. I did, however, get an answer problem: y'' + y = e^x + x^3, initial conditions y(0)=2, y'(0)=0...

I have put down the whole question and my answers which i would appreciate if someone could comment: Part 1.1 Find the general solution of the equation (d^2 z)/(dx^2 ) - 4 * dz/dx + 13z = 0 Put into form: a * m^2 + b * m + c ∴ m^2 - 4m + 13 = 0 a = 1, b = -4, c = 13 Then: m_(1,2 =...

Hello, i have a bit of a problem with uderestanding how exactly we use RK4 method for solving 2nd order ODE. And last conversation with my proffesor only added up to my confiusion. Further more i couldn't find any example dealing with this problem if any1 could provide link explaining this...

Homework Statement Could some mathematically minded person please check my calculation as I am a bit suspicious of it (I'm a physicist myself). This isn't homework so feel free to reveal anything you have in mind. Suppose I have two functions \phi(t) and \chi(t) and the potential V which...

Homework Statement y^{2}\frac{d^{2}y}{dx^2} + ay = b(cx-d) Find y as a function of x,a,b,c & d (a,b,c & d are all constant(!)) Homework Equations - The Attempt at a Solution Not a clue, this is actually how far I got with my own take on an orbital mechanics problem I made up...

y'' + 6y' + 4y = x(t) I found the eigenvalues to be -.764 and -5.24, no problems here. Next, since the order of the response is greater than the order of the excitation, I assumed the unit response took the form: h(t) = k_1e^{-.764t} + k_2e^{-5.24t} So now I must find the values for k_1 and...

Why is the characteristic of (d/dx) + (d/dt) = 0 where d is small delta c = x - t and not c = x + t

Homework Statement [PLAIN]http://img265.imageshack.us/img265/6778/complex.png I did the coefficient of the w' term. What about the w term? This seems like a fairly standard thing, but I can't seem to find it anywhere. What ansatz should I use for q, if the eqn is written w''+pw'+qw...

Homework Statement Find the solution of the following differential in the limit z -> i/2: Homework Equations Quotient rule, product rule. The Attempt at a Solution I found the first derivative using the quotient rule, with the answer as two fractions. I then took both fractions and...

Ok, so I've been studying the method of variation of parameters in order to solve 2nd order ODEs, and I have a question regarding a supposition that is made in the definition of the method. Say, y'' + p(t)y' + q(t)y = g(t) Then the general solution to the above equation is c_1y_1(t) +...

Homework Statement 1.a) Taking the Schrodinger second order differential equation given, split it into two first order differential equations for numerical solving. We're given the relevant constants in a table, such as \hbar, \alpha, etc. 'z' is taken to be an indepedent variable which we...

1. Using the complementary function and particular integral method find the solutio of the differential equation. d2y/dx^2 + 3 dy/dx +2y = 20cos2x Which satisfies y(0) = 1 y'(0) = 0 Homework Equations The Attempt at a Solution

Hi everyone, I'm having a hard time analyzing the following problem: b v(x) = -exp(-x) - 1/2 ( g v'(x) )^2 - n x v'(x) + S(g) v''(x) where: v' = dv/dx, etc. 0 < b< 1 g > 0 n > 0 S(g) >0 and S'(g) >0 x \in (-inf, inf) The main goal is to figure out what happens as g...

I recently attempted to solve the following: y” + (K/m)y = (Kl^{0}+mg)/m y(0) = l_{0} y(t_{e}) = (K l_{0}+mg)/K The Attempt at a Solution y(t) = -(mg/K)cos{\sqrt{K/m} t} + (mg/K){cos{\sqrt{K/m} t_{e}}/sin{\sqrt{K/m} t_{e}}}*sin{\sqrt{K/m} t} + (K l_{0}+mg)/K which...

I need help. For the following problem, can someone suggest how I should start on this question. I only have one quarter of diff eq classes plus a few classes in Fourier analysis. I'm out of my league. Consider a box with length, width and height given by L. The box encompasses the region...

I want to solve: y(x)''-(\frac{m\pi}{a})^2y(x)=0 With boundary condition y(0)=y(a)=0. First part is very easy using constant coef. which give: y(x)=c_1 cosh(\frac{m\pi}{a}x) + c_2 sinh(\frac{m\pi}{a}x) y(0)=0 \;\Rightarrow\; c_1=0 \;\Rightarrow\; y(x) = c_2 \; sinh(\frac{m\pi}{a}...

Homework Statement Consider the system of coupled second-order differential equations u''-(t+1)(u')^2+2uv-u^3=\cos{t} 2v''+(\sin{t})u'v'-6u=2t+3 with initial conditions u(0)=1, u'(0)=2, v(0)=3, v'(0)=4. Use the second order Runge-Kutta method with h=0.2 and a=2/3, b=1/3, \alpha=\beta=3/2...

So I have never solved a second order NON LINEAR ode before, but my current project has thrown one at me. I am going to use MATLAB to solve it when I have it in the correct state, but at the mo, I can't get it to that... Its three coulped equations, in terms of x,theta and x2. They are in a...

I want to know if there is a general solution to a second order homogeneous differential equation with variable coefficients?

I have the following equation d^2y/dx^2 +4dy/dx +8y = 4sin(2x) - 12cos(2x) y(0)=1 & y'(0)=-6 For the auxillary equation I have (m + 2)^2 = sqrt -4 which gives m=-2-2i & m=-2+2i Which gives y=e^-2x(Ccos(-2x) + Dsin(-2x)) Now to tackle particular integral. Try y=acos(2x) +...

1. The problem statement. Two 2nd order ODEs are given as : x''-2xy''+x^2 y' = 0 x"+y"+xy'+yx'=0 write a code to solve them numerically using RK4 in matlab. The Attempt at a Solution I have some idea of starting this kind of problem. That is, I first need to convert them into Four 1st...

I'm looking at a guide by Texas Instruments on active filter design. In it are the following equations for a second order lowpass filter, verbatim: The coefficient form of the denominator: s^2 + a_1s + a_0 Normalized: P(s) = (\frac{s}{\sqrt{a_0}*\omega_c})^2 + \frac{a_1s}{a_0*\omega_c} + 1...

I'm working on a computer programming project on matlab, and need an equation in the form of y'' + y' + y = 0 or k or inthe form of y' + y = 0 or k.. everything will be simple for me after that but I have these two equations N - ay'' - by' - cy - dx'' - ex' - fx = 0 M - gy'' - hy' - iy -...

I'm doing an undergrad research job.. I have encountered the following coupled 2nd order linear ODE with constant coefficients a, b, c, d... \begin{align} \frac{d^2 y_1}{d x^2} + a^2y_1 & = -c y_2 \\ \frac{d^2 y_2}{d x^2} - b^2y_2 & = -d y_1 \end{align} In addition, I...

Homework Statement y''x^{2} + 4xy' -y = ln(x) The Attempt at a Solution -I considered the quadratic characteristic equation, but it won't work because of the x^2 -I also tried variation of parameters. so i have v = y' and v'=y'' but i have no idea what i would sub when I get to y. any...

Homework Statement Solve \frac{d^2 u(x)}{dx^2}=x(1-x) subject to the homogeneous boundary conditions u(0)=0=u(1), using Green's functions. Homework Equations Green's functions... The Attempt at a Solution There are three parts: i - homogeneous eqn: \frac{d^2...

I'm not very experienced on heat laws and devices, other than general thermodynamics. But I am studying 2nd order systems, and the curiosity came up if there is a 2nd order thermo system, since my book only described a 1st order one. I see the thermal capacity as an electronics capacitor...

Homework Statement Find the general and, if possible, particular solutions of the following ordinary differential equations: y''+9y=36sin3x (hint: modification rule for PI) Homework Equations Knowledge of ODE's y = y_{aux}+y_{particular} The Attempt at a Solution I get the compementary...

{\frac {{\it du}}{{\it dx}}}=998\,u+1998\,v {\frac {{\it dv}}{{\it dx}}}=-999\,u-1999\,v u \left( 0 \right) =1 v \left( 0 \right) =0 0<x<10 Second Order Backward Difference formula {\frac {f_{{k-2}}-4\,f_{{k-1}}+3f_{{k}}}{h}} I'm trying solve this numerically in matlab, but can't seem to...

Homework Statement What's the general procedure for solving an i.v. b.v. ode of the form (d^2 T(x))/ (d x^2) = -c * e^T(x) T(+/-1) = 0 T'(0) = 0 where c is a constant Homework Equations i know from ode class that problems like this can usually be evaluated as T'' +...

Homework Statement \frac { d^2 \theta }{d x'^2 } = -y *exp(\theta) eq. 1 mayb be integrated to yield exp(\theta) = \frac {a}{cosh^2(b \frac{+}{-} \sqrt \frac{a*y}{2} * x')} \theta = f(y,x') Homework Equations The Attempt at a Solution the exponent is throwing me off, but i probably...

Homework Statement Let y be the solution of the initial value problem: y'' + 2y' + 2y = 0 , y(0) = 0 , y'(0) = 5 The maximum value of y over 0 less than or equal to x less than infinity is ??. The Attempt at a Solution r = -2 +/- i I solved it: y = c1 e^-2x cos(x) + c2 e^-2x sin(x) y' =...

Homework Statement Find the general soulution to : y'' = sin(2x) and the particular solution that satisfies: y(0) = −1/4, y(pi/4) = pi/2. Homework Equations y = c1y1(x) + c2y2(x) + yp(x) The Attempt at a Solution y'' = sin2x ----> y = -sin(2x)/4 -0.25C1sin(2x) - 0.25C2sin(2x)...