2nd order Definition and 494 Threads

To my knowledge I assume: Newton's second law of motion : F = ma = mx'' Hooke's Law F = ks where s is the distance displaced by the mass. When a mass is attached to the spring, the new spring force is: F = k(s+x) While the downward force is still: mg If the two forces...

"separation of variables", but for 2nd order Ok, I know how to separate variables in solving an ODE. I am unable to understand a solution I have for a problem which was the result of reduction of order- we end up with u''*sinx-2u'*cosx=0 so turn this into u''/u'=-2cosx/sinx At this point I...

Homework Statement Find the general solution to the following differential equation: \frac{d^2 y}{dt^2} - 2 \frac{dy}{dt} + 2y =e^t The correct answer must be: y(t) = C_1 e^t \cos t + C_2 e^2 \sin t +e^t The Attempt at a Solution I haven't been able to get the correct answer so far. The...

I got trouble in dealing with this kind of system. For example, Ay``+By`+Cy=0 where y=transpose(y1 y2) A=(1 0 0 1) B=(0 1 1 0) C=(1 1 1 1) May someone give me a book name?:smile:

2nd Order Homogenous ODE (Two solutions??) Alright. I understand that if we have a differential equation of the form A\cdot\frac{d^{2}y}{dt}+B\cdot\frac{dy}{dt}+C\cdot y = 0 and it has the solution y1(t), and y2 is also a solution. Then any combination of the two yH=C1y1(t)+C2y2(t)...

OK, a quick intro to the delayed choice quantum eraser is at wikipedia (http://en.wikipedia.org/wiki/Delayed...quantum_eraser ). I have attached a figure of the modified DCQE. In this setup there is no delay, there is no choice, and there is recombination of the idlers instead. In the...

I got some questions about this topic... y'' + p(z)y' + q(z)y=0 where y (and its derivatives) is a function of z, z ∈ ℂ. 1) My books says this: In points where both p(z) and q(z) are analytic, y(z) is also analytic. But in points where p(z) or q(z) (or both) aren't analytic, y(z) may not...

Homework Statement Find the voltage across the resistor. Homework Equations V = L*di/dt I = C*dv/dt The Attempt at a Solution I'm not too worried about the differential equation part but I need some help setting up the circuit for me to start the process. Since the current through the...

Hi I am trying to integrate Newtons equations for my system a = \frac{F}{m} = \frac{d^2x}{dt^2} This is only for the first coordinate of the particle. I wish to do it for y and z as well, but let us just work with x for now to make it simple. The force in the x-direction depends on...

General solution to a 2nd order differential :( Homework Statement What is the general solution of ∂2f(x,t)/∂x∂t = xt ? Homework Equations The Attempt at a Solution I have no idea, I tried to follow an example out of the book but it was quite different to this question. Do...

2nd Order differential equation, numerical method Homework Statement I've attached the question. Homework Equations The Attempt at a Solution u=y and v=y′ let y'=dy/dt = du/dt = v dv/dt = u'' therefore, dv/dt + 7(v)^2 +3x^2 *y^3 = 2 dv/dt = 2 - (7(v)^2) - (3x^2)*(u^3)...

THomework Statement Solve x*y'' + y' - a*y = 0 where a > 0 Homework Equations Not sure what's relevant here. See Below. The Attempt at a Solution I think this can be solved by changing the independent variable. I tried x = √t, x = 1/t, x = ln(t), x = exp(t) but these seem to...

I have a PDE in two variables, u and v, which takes the form \frac{\partial\psi}{\partial u\hspace{1pt}\partial v} + \frac{1}{r}\left(\frac{\partial r}{\partial u} \frac{\partial \psi}{\partial v} + \frac{\partial r}{\partial v}\frac{\partial\psi}{\partial u}\right) for an auxiliary...

Well, surely there is one unique solution to linear 1st order ODE and two linearly independent ones for 2nd order linear ODE, but can someone share the proof of this?

hello this question from my coarse notes has been giving me some trouble so i thought i would ask for some help on here, http://img88.imageshack.us/img88/9764/asfar.jpg i understand that since the bases are bases of the same solutions then they are just a multiple of each other, but...

hey guys i've been trying to work out this ode reduction question, http://img204.imageshack.us/img204/8198/asdawt.jpg after i use the hint and end up with a seperable equation then integrate to get \begin{align} & p=\pm \frac{1}{\sqrt{{{y}^{2}}-2c}} \\ &...

Hey, Every where I look I can only find books and pdf talking about the uniqueness and linear independence of the solutions but I haven't been able to find a procedure of finding the solutions to one of these ode's if you haven't been already given a particular solution. I've been trying...

My doubt is that is dimension of a 2nd order homogeneous equation of form y''+p(x)y'+q(x)=0 always 2 ? or dimension is 2 only when p(x),q(x) are contionuos on a given interval I..??

Homework Statement y'' + y' - 2y = 0 Homework Equations The Attempt at a Solution I think this is extremely simple. hopefully i am correct. i said the 'auxiliary' equation is r2 + r - 2 = (r+2)(r-1) = 0 the roots are r = 1, -2 so the solution is y=c1ex + c2e-2x correct?

y''-3y'+2y=e^t y(0)=0 y'(0)=-1 yh=solution to homogeneous equation (y''-3y'+2y=0) = Ce^t+Ae^(2t) C and A are constants yp=solution to particular solution (e^t) yp=ae^t where a is a constant. It turns out that this solves the homogenuous solution so I had to multiply it by a...

Homework Statement y''+6'+10y=0 y(0)=2 y'(0)=1 Homework Equations The Attempt at a Solution Laplace everything and I get s^2*Y(s)-2s-1+6s*Y(s)-12+10Y(s)=0 isolate Y(s) Y(s)=(2s+13)/(s^2+6s+10) split into 2 terms, bottom can be rearranged by completing the square...

2nd order DE..."largest interval" confusion Homework Statement Determine the largest t-interval on which therem 3.1 guarantees the existence of a unique solution: y'' + 3t^2y' + 2y = sin(t) ...y(1) = 1 ...y'(1) = -1 Homework Equations theroem 3.1 is the one that states if p(t)...

Hi, I need some help to find the analytical solution of the following DE: x" - k x/x' = at + b, with x' = dx/dt and x" = d(dx/dt)/dt Any kind oh help or advices on where I can find some useful resources are really appreciated. Thank you

Hello folks, I am attempting to implement an LQR controller to a quadrotor and in order to do this I need to linearize the model's equations about a certain trim point, in this case hover, which makes all initial conditions equal to 0. However I am having a lot of trouble linearizing these...

Homework Statement Find the solution to the following 2nd Order Differential Equation at x = 1: y'' = 10y -200 Boundary conditions: when x = 0, y = 100 when x = 1, y' = 10 2. The attempt at a solution Complimentary function: y = A exp{(10)^0.5 x} + B exp{- (10)^0.5 x} Particular Integral: 20...

Hel(lo, p) I hope you're doing fine I'm stuck with the following: y'' = -1/(y^2) I tried guessing functions (exponentials, roots, trigs... ) , but none worked, I haven't had any DE course, so I don't have specific steps to employ, I appreciate your help, Thanks in advance

Homework Statement I have a frequency equation to solve for the displacement for a spring mass damper truss system, as seen below, [m]u''+[c]u'+[k]u=f(t), where m,c,k, are all matrices (2x2), and f(t) is a graph-defined forcing function. I am to use 3 nodes, using the central...

Homework Statement solve: 160y''=160g-ky y(0)=-200 and y'(0)=0 2. The attempt at a solution I tried to use guess and check to solve this equation, but it didn't turn out nice at all... y''=9.8 - (ky)/160 y''+(ky)/160 = 9.8, guess y=e^(λt), y'=λe^(λt), y''=λ^2e^(λt) : this gives...

In the weak field approximation, g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu} If we make a coordinate transformation of the form [itex]x^{\mu'}=x^{\mu}+\xi^{\mu}(x)[\itex] it changes [itex]h_{\mu\nu}[\itex] to [itex]h'_{\mu\nu}=h_{\mu\nu}+\xi_{\mu,\nu}+\xi_{\nu,\mu}+O(\xi^{2})[\itex] I...

Homework Statement Ugh I feel really stupid for posting this but for some reason I can't remember how to solve it. I am trying to solve the diff eqn: D*\frac{d^{2}\phi}{dx^{2}} - \Sigma_{a}*\phi(x) = -q_{t} (thermal diffusion equation for neutrons slowing down to thermal energy) The...

Homework Statement yy''-y'^2 = y^2lny The Attempt at a Solution well, since the equation is of the form f(y,y',y'')=0 I turn it into the form f(y,p,p dp/dy)=0. After those substitutions are made, we'll have the following equation: yp (\frac{dp}{dy})-p^2-y^2 lny=0 which is a Bernoulli equation...

The question I'm trying to solve is: y" - 6y' + 9y = \frac{exp(3x)}{(1+x)} I formulated the Gen solution which are: y1(x) = exp(3x) and y2(x) = xexp(3x) I've then calculated the wronskian to get: exp(6x) I then went onto to use the variation of parameters formula, which is where...

Hello! I am answering a problem which involves spins in the hamiltonian. The hamiltonian is given by H = B(a1Sz^(1) + a2Sz^(2)) + λS^(1)dotS^(2). The Sz^(1) and Sz^(2) refers to the Sz of the 1st and 2nd spins respectively. B is the magnetic field and the others are just constants. The...

Hello, Does anyone know of a nonlinear 2nd order DE which must be solved numerically? I've got a new idea about how tackle it analytically... So I need one with a known solution to check my results.thanks!

What method can I use to analytically solve the following 2nd order PDE? u=u(x,t) ∂u/∂t - a*x*∂u/∂x-D*∂^{2}u/∂t^{2} = 0 I.C.: u(x,t=0)=u_i B.C.: u(x=+∞)=0 u(x=-∞)=1 Is self-similar the only way to solve it, or is there any other method can be used to solve it? How to set the...

Homework Statement I have a pde, 16d2u/dxdy + du/dx + du/dy + au = 0 where a is constant. Homework Equations The Attempt at a Solution I have tried to solve this pde using the substitutions x=e^t and y=e^s so t=ln(x) and s=ln(y) then finding Du/dx= 1/x du/dt and du/dy= 1/y...

Homework Statement For the following equation y" - λy=0 find the values of λ which produce a non-trivial solution on the interval 0 <= x <= a The given initial conditions are y(0) = 0 y(a) = 0 Homework Equations The Attempt at a Solution see attached pdfs My...

Homework Statement This is a portion of a slightly larger problem involving: K*\frac{d^2x}{dt^2} = -K2*\frac{dz}{dt} K*\frac{dz^2}{dt^2} = K2*\frac{dx}{dt} I would like to check my work and I don't believe I am moving toward the solution, knowing it has sin and cos in...

Homework Statement I must solve x(1-x)y''+4y'+2y=0. According to Boyce and Di Prima's book, Paul's note on DE on the internet and the notes of my professor, such a DE is homogeneous. However if I use the definition of homogeneous "f(tx,ty)=t^nf(x,y)", I don't find that's it's homogeneous of...

i have the first solution y_1(t) = t for (1-t)y'' + ty' - y = 0. I need to get the 2nd linearly independent using Abels theorem. the integration is messy but i have it set up (sorry no latex); y_2 = (t) * integral to t ( 1/s^2 * exp( -integral to t (s(s+1) ds) ) ds. Could anyone...

Homework Statement I am studying a forced undamped oscillator with MATLAB governed by the equation: y'' + \omegaoy = 2Cos(\omegat) First I have to write a function that can be solved by the solver ode45. Here is where I am stuck. Matlab just spits error messages at me when I try to...

The problem statement: Find the largest interval in which the solution of the following initial value problem is valid: cos(t/3)y'' +(6t^2)y' + ((t-5)^-3)y = 0 Initial conditions: y(1) = 1 y'(1)= 3 I have a few questions concerning this problem. I've converted it to it's...

The question is: Find a second order linear equation which has y1=-3e^(2t) and y2=e^(2t)+2te^(2t) as two of its particular solutions. Attempt at a solution: Since it's a repeated root problem, we know r=2, therefore the characteristic equation must look like (r-2)^2=0 r^2-4r+4=0...

If I solve a simple 2nd order ODE using a Fourier transform, I only get one solution. E.g.: \frac{d^2f}{dx^2}=\delta (2\pi ik)^2\tilde{f}=1 \tilde{f}=\frac{1}{(2\pi ik)^2} f = \frac{1}{2}xsgn(x) However, the general solution is f = \frac{1}{2}xsgn(x) + Cx + D Why do I...

I need to derive the solution for the differential equation analytically: y'' + g(t,y(t)) = 0 y'(0) = z_o y(0) = y_o I know the solution is: y(t) = y_o + z_ot - single integral from 0 to t of (t-s)g(s,y(s))ds I believe I need to assume something about the solution being a function...

Using the Frobenius Method -- 2nd order DE Homework Statement y"+(1/sinx)y'+((1-x)/x^2)y=0 Find the indicial equation and forms of two linearly independent expansions about x=0. Don't find the coefficents. Homework Equations The Attempt at a Solution The singular points at...

I was given the equation dp/ds = 4 + 1/e*d/de(e*dp/de) The derivatives in the equation are partial derivatives the values of p,s,e are dimensionless numbers. I am to assume that the solution is separable and then use finite difference method to solve for p, the finite difference method...

Homework Statement obtain the solution of the coupled system of equations d2X1+2X1=X2 d2X2+2X2=X1Homework Equations,The Attempt at a Solution I envisioned encountering this equation using matrix methods, as outlined in this website, since it was much easier than substitution, differentiation...

Homework Statement Solve the following forced D.E. (Show work) L=10 R=20 C=0.01 x(0)=10 x'(0)=0 Homework Equations This is the second order D.E. for a forced LRC circuit L(d2x/dt2)+R(dx/dt)+x/C=200sin(t) The Attempt at a Solution y=ygeneral+yparticular I calculated ygeneral...

Homework Statement y''+16y=3.36 This is actually part of a spring question I'm attempting at the moment, and I'm having a mental blank on how to deal with the 3.36.Homework Equations n/a The Attempt at a Solution I've found the characteristic equation and solution based from that; c_1...