Second order Definition and 602 Threads

Homework Statement The only singularities of the differential equation y''+p(x)y'+q(x)y=0 are regular singularities at x=1 of exponents \alpha and \alpha', and at x=-1 of exponents \beta and \beta', the point at infinity being an ordinary point. Prove that \beta=-\alpha and \beta'=-\alpha'...

Homework Statement a. Compute the second order Taylor polynomial centered at 2, P2(x), for the function ln(x). b. Estimate the maximum error of the answer to part a for x in the interval [1,2].Homework EquationsThe Attempt at a Solution For part a, I'm thinking that when it says "second...

Homework Statement Hi, It's been a while since I have taken differential equations. How do I solve an equation like this: k_{1}\frac{d^{2}V_{x}(t)}{dt^{2}}+k_{2}\frac{dV_{x}(t)}{dt}+k_{3}V_{x}(t)=0 Homework Equations The Attempt at a Solution I have looked through my...

1. For this problem, we are asked to design a MatLab/Octave code that will calculate and plot the orbit of a sattelite 2. We are given the following 2nd order equations x''= \frac{-x}{( \sqrt{x^{2}+y^{2}})^{3}} y''= \frac{-y}{( \sqrt{x^{2}+y^{2}})^{3}} We can convert this into the...

hey all, i'm stuck with the following designing problem (Control course) : Homework Statement given the location of the poles , find rise time , peak time, percentage maximum overshot and settling time for each pole. pole are: 1 . pole at θ = 70 , ωn = 1 2. pole at θ = 70 , ωn = 3...

How to solve a system of 200 second order differential equations in matlab? I know simulink can work but it takes damn long time to draw those blocks for 200 equations...

Homework Statement Hi there guys I am new to this forum and i have a problem with a bit of cw. It's regarding an RLC circuit. I've come up with a picture (attached) that denotes the equation. Homework Equations I know the equation is L C \frac{d^2 i}{d t^2} + \frac{L}{R} \frac{di}{dt}...

Homework Statement Find v(t) for all t>0. Use second order method. Homework Equations The Attempt at a Solution Before the switch is closed: solving for i: -80+160i+80i+80i=0 i=0.25A KCL: From node v(t): [C dv(t)/dt] + i(t) + [V(t)/4] + [(v(t)-80i)/80]+[(v(t)-80)/160] = 0...

I must say I'm utterly confused with the Annihilator method for solving Non-Homogeneous Constant Coefficient Second order O.D.Es. I guess it'd be better to list out my questions:- 1. Is it possible to find an annihilator for every single function out there? I mean, is it always possible to...

Hello there, I am facing the second order ODE in the unknown function $$y(t)$$ $$ \ddot{y} = a \dot{y} y - b \dot{l} l - c\dot{l} + d$$ $$a, b, c, d$$ positive constants, such that $$ \frac{a}{b} = \frac{d}{c}$$ I would like to understand more about it before relying on numerical methods...

I encountered the following second order nonlinear ODE while solving a problem in electrostatics. The ODE is: \frac{d^{2}V}{dx^{2}} = CV^{-1/2} How can I solve this? Regards. Homework Statement Homework Equations The Attempt at a Solution

Homework Statement Given y_1(x)=x is a solution to (2x-1)y''-4xy'+4y=0, find y(2) given (y(1),y'(1))=(0, 0). Utilize method of reduction of order. I need help with this as I end up getting some ugly (in my mind, anyways) integrals. Thanks in advance!The Attempt at a Solution Let y=y_1v=xv...

given that y = 2 at x = 0 and \frac{dy}{dx} = -5 at x = 0, find y in terms of x given further that \frac{d^2y}{dx^2} + \frac{dy}{dx} = 2x +3 finding the complementary function: m^2 + m = 0 m(m+1) = 0 m = 0, m = -1 so complementary function y = A + Be^(-x) Particular...

If have this equation: \frac {d^2x}{dt^2}=-\frac{x}{1+x^2} How do I solve it?

h''(t)=-\frac{1}{h(t)^2}, h(0) = h_0, h'(0)=v_0 The first step is to, I think, reduce this to a fist-order problem: h'(t)h''(t)=-h'(t)\frac{1}{h(t)^2} --- Multiply both sides by h'(t) h'(t)^2=\frac{1}{h(t)}+c_1 --- Integrate both sides 1/h'(t) = \sqrt{\frac{h(t)}{c_1 h(t)+1}} ---...

While studying the derivation of the normal modes of oscillation of a liquid sphere in the paper "Nonradial oscillations of stars" by Pekeris (1938), which can be found here, on page 193 and 194 two coupled second order differential equations in two variables are merged into one fourth order...

Hi all, I have a nonlinear ODE in the following form: a x'' + b |x'|x' + c x' + d x = y where x and y are functions of time and a,b,c and d are constants. As far as I can tell the only way to solve this is numerically, something I've managed to do successfully using a Rung-Kutta scheme...

Suppose we have two multivariate functions, u_{1}(x,t) and u_{2}(x,t). These functions are solutions to second-order linear equations, which can be written as follows: Au_{xx}+Bu_{xy}+Cu_{yy}+Du_{x}+Eu_{y}+Fu=G Each of the coefficients are of the form A(x,y). Now, the linearity of these...

This was a lecture example and it has confused me. Can someone please help explain it? If we have the following fist order system: τ.dx/dy+y(t)=x(t) where τ=c/k where "k" is the spring stiffness and "c" the linear damper coefficient and τ is a time constant. For the unforced case x(t)=0, we...

second order pde -- on invariant? What the meaning for a second order pde is rotation invariant? Is all second order pde are rotation invariant? or only laplacian?

Homework Statement The Second Order Differential Equation is: x''-u(b^2 + x^2)x'+x=0 Initial Conditions are: x(0)=1 x'(0)=0 It is to be numerically solved for 0<=t<=500. The specific numerical method to be used isn't specified, but it must be programmed into c. As a means to check the...

I'm having some difficulties figuring out how to linearize second order differential equations for a double pendulum. I have an equation that is in the form of \theta_{1}''\normalsize = function [\theta_{1},\theta_{2},\theta_{1}',\theta_{2}'] (The original equation is found at...

Homework Statement basically solve \frac{d^{2}y}{dx^{2}} + 4\frac{dy}{dx} + 4y = cos2x Boundary conditions are y=0, dy/dx =1 at x=0 Homework Equations The Attempt at a Solution I am having trouble getting the coefficients to the solution. I got the complementary function as...

What is the solution of the follwoing differential equation \frac{\partial^{2}y}{\partial x^{2}}-ay^{-1}\frac{dy}{dx}=0 where a is a constant.

Hello, I have read that, in a freely-falling frame, the metric/ interval will be of the form: ds2 = -c2dt2(1 + R0i0jxixj) - 2cdtdxi(\frac{2}{3} R0jikxjxk) + (dxidxj(δij - \frac{1}{3} Rikjlxkxl) to second order. Does anyone know where I could find a derivation of this result?

Hello! I am trying to solve the following second order PDE (copy that into mathematica): \!\( \*SubscriptBox[\(\[PartialD]\), \(x, t\)]\(\[Delta][x, t]\)\) + b \!\( \*SubscriptBox[\(\[PartialD]\), \(t\)]\(\[Delta][x, t]\)\) + a \!\( \*SubscriptBox[\(\[PartialD]\), \(\(x\)\(\...

I know how we solve ODE's and euler equations in which we have cos and/or sin terms on the right. We take the particular solution to be Acos(x) + Bsin(x). But what if we have secant or cosecant terms on the right or tan and/or cotangent terms? Qno. 1 Are these 4 terms possible i.e. can they...

I don't understand where the A and B come from, if y = e^(mx), would the general solutions be y = Ae^(mx) + Be^(m_1x) assuming there are two distinct roots of the auxiliary equation? If anyone could clear this up, thanks.

Homework Statement I must solve ##y''+2y'+2y=e^{-t}\sin t##. I know variation of parameters might not be the fastest/better way to solve this problem but I wanted to practice it as I never, ever, could solve a DE with it. (Still can't with this one). Though the method is supposed to work...

Homework Statement Hello guys! I've never dealt with an ODE having 2 singularities at once, I tried to solve it but ran out of ideas. I must solve ##(x-2)y''+3y'+4\frac{y}{x^2}=0##. Homework Equations Not sure. The Attempt at a Solution I rewrote the ODE into the form...

Homework Statement Find the general solution of the ODE $$ y'' + 16y = 64x \cos x.$$ If ## y(0)=1, y'(0) = 0##, what is the particular solution? The Attempt at a Solution I am confident I can tackle this question, I really just want to check that my particular integral form is correct. I...

Homework Statement given: dt=-\frac{1}{2}\sqrt{\frac{l}{g}}\frac{d\theta}{\sqrt{sin^2(\alpha/2)-sin^2(\theta/2)}} make the change of variables sin(\theta/2)=sin(\alpha/2)sin(\phi) to show that: dt=-\sqrt{\frac{l}{g}}\frac{d\phi}{\sqrt{1-k^2sin^2(\phi)}} where k=sin(\alpha/2) Homework...

I know that if ##Y_1## and ##Y_2## are two solutions of a nonhomogeneous second order differential eqn, then ##Y_1 - Y_2## is also a solution. So this motivates the following: if we set ##Y_1 = y(x)##, where ##y(x) ## is an arbritary soln of the nonhomogeneous ODE and ##Y_2 = y_p(x)##, some...

http://imgur.com/6aAMV So I need to find the current labeled as a function of time. THe switch opens at t=0 and I drew the circuit after the switch opens. I found the initial current to be -4 and the voltage on the capacitor to be 8. I'm having trouble trying to find di_L(0)/dt. I...

Suppose there's a system with given uncertain parameters. And I would like to obtain certain Rise time, max. over shoot, settling time by adjusting those parameters. Let's say this is the second order system; T(s) = (ks + c) / (s2 + as + b) First of all; for a second order system there...

I am having a problem finding the solution for this eq: y''(x)+(2/x)y'(x)+(w^2)y(x)=0 I couldn't find examples in the textbook that goes on a similar line, and have been searching the internet as well, but no use. I am thinking of using substitution v=y' but not sure how to do that in the...

Not sure if this topic belongs here, but here goes. Homework Statement From the AP physics C 1995 test there is a problem that gives the potential energy curve U(x). With F=-\frac{dU}{dx} in one variable, F(x)=-\frac{a}{b}+\frac{ba}{x^{2}} Where a and b are constants. Now I need to get...

Homework Statement Hello guys. I've been stuck on a problem when searching for the Green function. Here is the problem: Find the solution of x^2 y''-2y=x for 1 \leq x < \infty with the boundary conditions y(1)=y(\infty ) =0, using the appropriate Green function.Homework Equations The general...

Homework Statement When solving a D.E. with power series, I've encountered something along the lines of: (2 - r)^{2}g'' = -2 Homework Equations Power Series The Attempt at a Solution I know I am just supposed to assume such a series exists, and work from there. But I'm really...

Homework Statement I have to draw the step response of the following two systems. G1 = (4+3s)/(s^2+4s+4) G2 = 3/(s^2+4s+4) So I started to draw the step response of the second system first. It has to be in the funky standard form: \frac{ω2}{s2 + 2ζωs + ω2} EDIT: Seems like the above doesn't...

Four days ago on mathhelpforum.com the user ssh [I don’t know if he the same as in MHB…] has proposed the following second order complete linear ODE… $\displaystyle y^{\ ''} – \frac{2+x}{x}\ y^{\ ’}\ + \frac{2+x}{x^{2}}\ y = x\ e^{x}$ (1) … and till now no satisfactory solution has been...

I was wondering what a guess would be for the particular solution of the right hand side of an equation if it looked like this: x^{2}y" - 4xy' + 6y = ln(x) My textbook has some specific examples of the right side function along with the corresponding form of the particular solution...

I was given the following equation to solve: x^2*y'' + x*y' + k^2*x^2*y = 0 B.C. y'(0)=0, y(1)=0 where k is just some constant. I am having a hard time removing the singularity created by the boundary condition at y' and not aware of a method how. Any advice would be greatly appreciated.

How to solve \( (x+1) y'' - (2x+5) y' + 2y = (x+1) e^x\) can we assume \(y_1 = (Ax+B) e^x \), then \(y_2= vy_1​\) Is this right? then solve for A and B Finally \( y = c_1 y_1 + c_2 y_2\)

Homework Statement I'm pretty sure this is a typo? http://gyazo.com/802746486cc68852e5384d5a12aed596 Homework Equations See the image ^. The Attempt at a Solution I believe the theorem they're talking about, is that you can write the general solution of a second order ODE : L[y] = y'' +...

Homework Statement A simple series circuit has an inductor of 1 henry, a capacitor of 10^-6 farads, and a resistor of 1000 ohms. The initial charge on the capacitor is zero. If a 12V battery is connected is connected to the circuit, and the circuit is closed at t=0, find the charge on the...

Hi all, I was wondering is you could help me with this springs question. We've only done springs hanging from a fixed support above being stretched, but now I've got a question where the spirng is being compressed. Homework Statement So, here's some basic info about the question...

Homework Statement Hi, this problem is from first chapter of Mathematical Methods of Physics by Mathews and Walker. (Problem 1-36, second edition) Consider the differential equation y'' - xy + y^3 = 0 for large positive x. a-) Find an oscillating solution with two arbitrary constants. b-)...

Homework Statement Let's say that we have a second order polynomial function, and we know all of the points where it intersects with the x and y axis. Ex: (-2; 0), (0; 2), (1; 0) How does on determine the ax^2+bx+c polynomial form based on that? Homework Equations - The Attempt at...

Homework Statement y''+4y'+6y y(0) = 2; y'(0) = 4 Homework Equations \alpha ± β = e^{x\alpha}(cosβx + sinβx) The Attempt at a Solution Auxilary equation is r^2+4r+6, which solves for -2 ± i I get the general solution: e^{-2x}(c1cosx + c2sinx) y' = -2e^{-2x}(c1cosx +...