Second order Definition and 602 Threads

Someone know how to uncouple this system of pde? Δu_{1}(x) + a u_{1}(x) + b u_{2}(x) =f(x) Δu_{2}(x) + c u_{1}(x) + d u_{2}(x) =g(x) a,b,c,d are constant. I would like to find a solution in one, two, three dimension, possibily in terms of Green function...someone could help me, please?

To Solve y’’ – 2 y’ – 3y = 64 e-x x ---------------(1) Using the method of undetermined coefficients : The roots of the homogeneous equation are 3 and -1, so the complimentary solution is y = c1 e3x + c2 e-x Then the guess for the particular solution of (1) is e-x x (Ax + B)...

$(1-x^2)y'' - xy' + 4y =2 x \sqrt{1-x^2} $ Hint use the substitution $x =\sin t$ I used it and end with $\cos t y'' + \sin t y' - \frac{\sin t}{\cos t} y' + 4y = 2\sin t |\cos t| $ how to solve this i just want the name of the method

Homework Statement Find the values of α for which all the solutions of y''-(2α-1)y'+α(α-1)y=0 (a) tend to zero and (b) are ilimited, when t->∞. Homework Equations y''-(2α-1)y'+α(α-1)y=0 => (t)=Ae^{αt}+Be^{(α-1)t} The Attempt at a Solution I found that the general solution to the...

1. y''y^4 = 8 I tried almost every method I know, including laplace transforms, variation of parameters, reductin of order, v=y' substitution

Hello everyone! I am fairly new to SDE theory, so I'm sorry if my question may be a bit naive. I have the following coupled set of SDE:s d\phi = \frac{v - v_r}{R}d t + \frac{\pi}{\sqrt{t_c}}d W d v = A\cos(n\phi - \phi_w)d t + a_v d t + \sigma_v d W. W denotes a Wiener process, and the...

Homework Statement Hi everyone, I have the following differential equation that I am trying to solve: (-1/k^{2})*(d^{2}y/dx^{2}) - y = (Q*c/P*L)*x Where Q,c,P,L, and k are constants. The solution ends up being: y = A*cos(k*x) +B*sin(k*x) -(Q*c/P*L)*x Where A and B are constants...

I was wondering what the common methods for solving such a system are: 2 m \ddot{x} - m l \ddot{θ} θ + k x = 0 m l^{2} \ddot{θ} - m l \ddot{x} θ + m g l θ = 0

Hi Everyone, I was reading a paper and I found it hard to comprehend how some of the equations were arrived at, probably because my math rottenness. Anyway I need your help on understanding how these equations were arrived at. The problem goes like this: We have this PDE in cylindrical...

Hello, I tried to find the non linear second order differential solution of: diff(y(t), t, t)-(diff(y(t), t))+exp(y(t)) = 0 can anyone please help me? Kind regards, JJ

What is it?! I have tried plotting dummy data showing y values halving as x values double and no simple type of equation results (ie exponential, power, polynomial etc) - is this true? I thought such a standard function would be a simple one!

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...

Hello Experts I have a simple question. Given V as the function of Z and Y, Given Z as the function of R and L, Z=R+s*L Given Y as the function of G and C, Y=G+s*C Assume we also know \frac{\partial V}{\partial Z} and \frac{\partial^2 V}{\partial Z \partial Y} If we want to know...

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...