Second order Definition and 570 Threads

How is uncountability characterized in second order logic?

Homework Statement Solve the following initial value problem: \frac{d^2y}{dt^2} + 2 \frac{dy}{dt}+y = t y(0) = 1, \ y'(0) = 0 The correct answer must be: y(t)=3e^{-t} + 2 t e^{-t} + t -2 The Attempt at a Solution Where did they get the term 2te-t from? Here's how I've done it so far...

I've tried with Goldstein but no luck, i need to understand how the constraint, especially the second class act on system, i also referred Dirac's lecture, they were quiet good, but if u can suggest some books which can help me learn first and second class constraints with examples and problems...

]Homework Statement Trying to get a good start on a second order, non-homogeneous, linear differential equation with constant coefficients. The differential equation is y”-4y’+4y=(1+x+x2+x3)e2x y(0)=1; y’(0)=0 The constraints with this problem is that I cannot use Laplace transform to...

Homework Statement 1)Calculate the general solution of y''+\frac{y'x}{1+x}-\frac{y}{1+x}=1+x. 2)What behavior do the solutions have in x=-1? 3)Solve the boundary problem to the DE in the interval [0,1] with y(0)=0 and y(1)+y'(1)=0. 4)Write down the DE under Sturm-Liouville's form and find a...

The question requests that I solve the circuit below for v0(t). I'm solving for the voltage over the inductor. I'm getting a result that's close to what I expect, however I think the phase angle of the voltage is slightly off (some friends of mine said they all got 46°, whereas I am consistantly...

I've completed my Engineering but doing a self study course in Dynamics of Structures and have got a very fundamnetal question concerning solution of differential equation and hope someone will be able to help me. Sorry if its too fundamnetal and stupid! Let us say we have to solve a...

Homework Statement How to find the initial capacitor voltage if the capacitor is in series with a 1.5 ohm resistor, these 2 are in parallel with a reversed polarity 6v DC source, (reversed polarity - the negative terminal is pointing up) i assume the voltage across the resistor and capacitor...

Homework Statement finding the general solution. I would like to know if the 20-e^x will be treated as a sum of a polynomial? Homework Equations The Attempt at a Solution

Is it possible to solve the following differential equation analytically? y''(x) = A - B [exp(y(x)/C) - 1] where A, B and C are constants. Thank you...

Homework Statement Find the set of functions from (-1,1)→ℝ which are solutions of: (x^{2}-1)\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}-4y = 0 Homework Equations The Attempt at a Solution There is a hint which says to use the change of variable: x=cos(θ) doing this I get...

See attached diagram. Taking downward as postive. The particle is pulled down past its equiliburm position (e=l) by l/2 and then released. It has mass m and is subject to a resistive force R. Why is it that the equation is mg - T - R = ma [1] as a pose to mg - T + R = ma.[2] I...

Homework Statement I have the equation mx'' + cx' + kx = 0 where m = 2, c = 12, k = 50, x0 = 0, x'(0) = -8. x is a function of t, and primes denote derivatives w.r.t. t. Homework Equations The Attempt at a Solution so the equation is 2x'' + 12x' + 50x = 0, which I simplify...

Hi guys I was hoping if someone could help me with this second order differential equation which i have to reduce into a series of first order equations and then solve using a fourth order runge kutta method. The equation is y"-30y'-3y=-2 with the initial conditions y(1)=-12 and...

Homework Statement Verify that y_1=x^3 and y_2=|x|^3 are linearly independent solutions of the differential equation x^2y''-4xy'+6y=0 on the interval (-\infty,\infty). Show that W(y_1,y_2)=0 for every real number x, where W is the wronskian. Homework Equations theorems on...

Homework Statement Find the set of functions from (-1,1)→ℝ which are solutions of: (x^{2}-1)y''+xy'-4y = 0 Homework Equations The Attempt at a Solution OK, I'm not really sure how to go about solving this equation, I have only previously attempted problems where the functions in...

Please see the attached description of the problem I need to split the second-order o.d.e to two first-order o.d.e's. (numerically) Then use the shooting method with a 0.5 step size to solve the system of equations. (This needs to be done on an excel spreadsheet) Then to plot the temperature...

Im trying to solve this problem, but i rally do not know where to start and i am having a lot of trouble. Vo" + 2Vo' + Vo = 10sin2t and Vo(0)=2, Vo'(0)=0 any help is much appreciated

Homework Statement The problem is to solve: y''-2y'+5y = e^{x}(cos^{2}(x)+x^{2}) Homework Equations The Attempt at a Solution I (think I) have solved the associated homogeneous equation: y''-2y'+5y = 0 giving the solution as: y_{h} = e^{x}(C_{1}cos(2x)+C_{2}sin(2x))...

Homework Statement Solve the ODE with the boundary conditions given Q''+Q = Sin(2x) where Q(0) = 1 and Q'(0) = 2 So i know i need to solve the general and particular solutions, however, I am a little confused. Any help or advice would be great, Thanks in advance. Homework Equations Y...

Hi there. This is my first time working with tensors, so I have to break the ice I think. I have this exercise, which I don't know how to solve, which says: If V=V_1...V_n is a first order covariant tensor, prove that: T_{ik}=\frac{\partial V_i}{\partial x^k}-\frac{\partial V_k}{\partial x^i}...

What is the difference between second order zero bode plot and second order pole bode plot?

Hi there. I have this exercise, which says: Demonstrate that: xy''+(1-x)y'+\lambda y=0 has a polynomial solution for some λ values. Indicate the orthogonality relation between polynomials, the fundamental interval, and the weight function. So I thought I should solve this using Frobenius...

Homework Statement \sin\theta\frac{d^2y}{d\theta^2}-\cos\theta\frac{dy}{d\theta}+2y\sin^3\theta=0Homework Equations Use the substitution x=\cos\thetaThe Attempt at a Solution I started off by listing: x=\cos\theta\\ \frac{dx}{d\theta}=-\sin\theta\\ \frac{d^2x}{d\theta^2}=-\cos\theta\\ But...

I semi understand the reduction of order method, and i understand the general solution for a 2nd order with repeated roots. however, i can't seem to form up the correct thing to solve this question, and research again proves futile. Any assistance will be appreciated. Use the method of...

Homework Statement Need to solve xy''+y'+xy=0 using Runge Kutta on x[1,3] Couldn't find algorythm to solve second order ODE using this method I know how to do 1st order Homework Equations The Attempt at a Solution I know I have to make this equation into 2 first order ODE...

I was given a question and i am really unsure how to go about solving it. it appears to be solveable using the characteristic equation and whatnot, however i have my coeffecients in terms of the independent variable. so i am confused. the question initially asked to compute the wronskian, and it...

Hi there. I have this differential equation: x^4y''+2x^3y'-y=0 And I have to find one solution of the form: \sum_0^{\infty}a_nx^{-n},x>0 So I have: y(x)=\sum_0^{\infty}a_n x^{-n} y'(x)=\sum_1^{\infty}(-n) a_n x^{-n-1} y''(x)=\sum_2^{\infty}(-n)(-n-1) a_n x^{-n-2} Then, replacing in the diff...

How do you prove that there does not exist numbers a,b\in\mathbb{Q} such that 0 = a + b\sqrt[3]{2} + \sqrt[3]{2}^2

Help solving a second order ODE with repeated roots, urgent! I have a differential equaition d2y/dx2 - 6dy/dx + 9y = 0 I have found the general solution to be y = (Ax + B)e3x Now I need to find the solutions to A and B so that... when y = 4, x = 0 when y = 49.e15, x = 5 I...

Homework Statement Find the Riemann function for uxy + xyux = 0, in x + y > 0 u = x, uy = 0, on x+y = 0 Homework Equations The Attempt at a Solution I think the Riemann function, R(x,y;s,n), must satisfy: 0 = Rxy - (xyR)x Rx = 0 on y =n Ry = xyR on x = s R = 1 at (x,y) = (s,n) But I...

Homework Statement Classify the equation and use the change of variables to change the equation to the form with no mixed second order derivative. u_{xx}+6u_{xy}+5u{yy}-4u{x}+2u=0 Homework Equations I know that it's of the hyperbollic form by equation a_{12}^2 - a_{11}*a_{22}, which...

Homework Statement Show that if F is twice continuously differentiable on (a,b), then one can write F(x+h) = F(x) + h F'(x) + \frac{h^2}{2} F''(x) + h^2 \varphi(h), where \varphi(h) \to 0 as h\to 0. Homework Equations The Attempt at a Solution I'm posting this here...

In cullen-zill chapter 6 equation 23 it says that y_{2}(x)=y_{1}(x)\int\frac{e^{-\int P(x)dx}}{y_{1}^{2}(x)}dx is a solution of y''+P(x)y'+Q(x)y=0 whenever y_{1}(x) is a known solution Where does this come from? I would like to be able to prove this or find a proof somewhere. My...

Homework Statement We're supposed to prove that y_{n+1} = y_n + \frac{k_1 + 2k_2 + 2k_3 + k_4}{6} k_1 = hf(t_n, y_n) k_2 = hf(t_n + \frac{h}{2}, y_n + \frac{k_1}{2}) k_3 = hf(t_n + \frac{h}{2}, y_n + \frac{k_2}{2}) k_4 = hf(t_n + h, y_n + k_3) f(t, y) = \frac{dy}{dt} is equivalent to...

Hey all, there is something that has always bugged me in linear second order ODEs. We say that the general solution is: y=C_1e^{r_1x}+C_2e^{r_2x} where r_1 and r_2 are the solutions of the characteristic polynomial. The cases where r1, r2 are real are pretty straightforward. If they are...

Homework Statement 3\frac{d^{2}y}{dx^{2}} + 2\frac{dy}{dx} + y = 0 Homework Equations The Attempt at a Solution 3y'' + 2y' +y = 0 I know the solution is going to be in the form of y=Ce^{mx}+De^{nx}+... (Unless there is a multiplicity, in which case I understand that too) So I'll just skip...

I'm not sure exactly how to solve this ODE. (dx^2)/(dt^2) + (w^2)x = Fsinwt, where x(0) = 0 and X'(0) = 0. What I've got so far is: x'' + w^2x = Fsinwt --> x(homogenous) = Acoswt + Bsinwt I know I have to find a particular solution but I keep getting zero as a result which I know won't...

Homework Statement Consider the transfer function H(s)=\cfrac{1}{a_{2}s^{2}+a_{1}s+a_{0}} where real-valued coefficients a_{2},a_{1}, a_{0} are arbitrary except that a_{2} is nonzero. Verify that the system is stable iff the coefficients a_{2},a_{1}, a_{0} have the same sign. Homework...

Homework Statement Solve x^2y''-3y=x^3. Show that there are many solutions \phi such that \phi (0)= \phi '(0)=0.Homework Equations Not sure.The Attempt at a Solution It's a Cauchy-Euler equation so that I made the ansatz \phi (x)=x^\alpha. I reached that x^\alpha [\alpha (\alpha -1 )-3]=x^3...

hello i need help with this, what is the differential equation for the voltage v2 (t). http://www.imageurlhost.com/images/mc2qqp4kax37kvm51h1h_circuit.jpg sorry for my english

Homework Statement For the differential equation y'' - 4y' + y = 0, (a) Show that if we let x = y' (i.e. x(t) = y'(t)), then this leads to the system: x' = 4x -y y' = x (b) Conversely, show that the system in (a) leads to y'' - 4y' + y = 0 (and x'' -4x' + x = 0 also). Homework...

Homework Statement Vibration in a system can be a source of problems. For example, the deck on a ship could vibrate due to the engine which represents a forcing function. This system may be simply modeled by a mass, representing the deck, a spring representing the stiffness of the deck and a...

Homework Statement Hello all, Representing RLC circuits via differential equations is rather new to me, in fact differentials as an entirety are new for me. Essentially I am looking for clarification regarding this type of question and whether or not I am doing it right. Thanks in advance...

If ay+b\int^y_0ydy+cy'=0 then ay'+by+cy''=0 now, let y=e^{sx} thus, s^2+a/cs+b/c=0 and then one solves for s. It is then plugged into what sources are deeming a "general solution" y=C_1e^{s_1x}+C_2e^{s_2x} however, none of these texbooks explain or derive where this comes from, and I have not...

Hi. I am new to differential equations. This is probably pretty easy but I don't quite understand how to do it yet. The equation is y^4 -3y'' -4y = 0. I can figure out what class of equation it is. I can write it in the form y'' = F(y), but I am not really sure how to solve it.

Homework Statement Given that the surface (x**5)(y**2)+(y**5)(z**3)+(z**3)(x**2)+4xyz=7 has the equation z=f(x,y) in a neighbourhood of the point (1,1,1) with f(x,y) differentiable, find the derivatives (∂**2f)/(∂x**2) at (1,1) Homework Equations The Attempt at a Solution I...

Homework Statement Use the method of undetermined coefficients to find one solution of http://img85.imageshack.us/img85/6844/4ab921ad6ba6851cc91401c.png Note that the method finds a specific solution, not the general one. Homework Equations Y = Yc + Yp Yc = C1e^(r1t)+C2e^(rt) when...

Homework Statement Solving the linked set of ODEs: y" + y = 1-t^2/π^2 for 0 ≤ t ≤ π y" + y = 0 for t > π We are given the initial condition that y(0) = y'(0) = 0, and it is also noted that y and y' must be continuous at t = π Homework Equations See above. The Attempt at a...

Calculate f" for f(x)=g(e^(2x)), where g is a function defined for all real numbers & g admits second order derivative. please check if I did it right. f = g(e2x) f' = 2e2x g' f'' = 4e2xg' + 2e2xg'' I have expanded out 4e2xg'(u) + 2e2xg''(u)