Second order Definition and 602 Threads

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)

Hi, I am trying to solve a second order nonlinear eqn which is y''+3y'=1/(y^5), y'(0)=0, using mathematica. When I type DSolve[y''[x]+3*y'[x]=(1/(y[x])^5) ,y'[0]==0,y[x],x]; I get "second-order nonlinear ordinary differential equation" as a result. I don't understand what mistake I am making...

Homework Statement y''-2y+y=xe^xlnx The Attempt at a Solution I don't know what I should do here because lnx. Is it possible to solve this ODE with undetermined coefficients method? how can I solve it?

Homework Statement Find the solution to :y''+2y'+y=t Homework Equations Suppose y(t)=B1t2+B2t+B3 And I believe, Y(t)=Yh+Yp. That is the solution is equal to the solution to the homogenous equation, plus the particular solution. The Attempt at a Solution First Solve the...

Homework Statement Refer Attachment. I am trying to derive the second order equation using the natural response of the circuit Homework Equations Refer Attachment The Attempt at a Solution Nodal Analysis: v1+\frac{1}{2}\frac{dv1}{dt}+\frac{1}{3}\frac{dv2}{dt}=0 Mesh Analysis...

Homework Statement Hi, I have to solve a boundary condition problem but therefore I have to integrate a second order partial derivative. However, I don't know how to integrate the equation two times. Can someone explain this step by step how I get this solution? Homework Equations...

Hello, I am having a little trouble solving this equation: \frac{d^2y}{dx^2} + \frac{A}{y}(\frac{dy}{dx})^2 + \frac{B}{(y+C)^2} = D - Ex where A, B, C, D, and E are constants and, sadly, not related. So far, I've found this http://eqworld.ipmnet.ru/en/solutions/ode/ode0344.pdf...

Homework Statement Consider the second order wave equation u_{tt} = 4u_{xx} There are initial and boundary conditions attached, but I'm less concerned with those for the moment. I think I can figure those out if I can figure out where to get started. Rewrite this as a system of first order...

Hello all. I am having a very serious problem. The question states: Find the value(s) of δ such that the solution of the initial-value problem y'' − 4y = sin x; where y(0) = δ and y'(0) = 0 is bounded. I have no problem "solving"...

Homework Statement The DE y''+\frac{2}{x}y'+ \left [ K+\frac{2}{x} - \frac{l(l+1)}{x^2} \right ]y=0, 0<x< + \infty. appears when working on the hydrogen atom. Find all the values of K (the eigenvalues) that generates solutions of the form \phi (x) such that \phi (x) remains finite when x...

Homework Statement I have found the general solution to a second order pde to be U(x,t) = f(3x + t) + g(-x + t) where f and g are arbitrary functions I have initial conditions U(x,0) = sin(x) Du/dt (x,0) = cos (2x) The Attempt at a Solution I have found that U(x,0) = f(3x) +...

d^{2}u/ds^{2}= cosu[(du/ds)^{2} - k^{2}]

Homework Statement I have a PDE for which i have found the general solution to be u(x,y) = f1(3x + t) + f2(-x + t) where f1 and f2 are arbitrary functions. I have initial conditions u(x,0) = sin (x) and partial derivative du/dt (x,0) = cos (2x)Homework Equations u(x,y) = f1(3x + t) + f2(-x +...

Hello! I was reading the proof (I think it constitutes a proof) for second order homogeneous recursive relations from the book Discrete Mathematics with Applications by S. Epp, and it seems, to me at least, to be excessive; which suggests that I don’t understand the proof. It goes...

Homework Statement Find a general solution to \frac{d^2x}{dt^2}-2\frac{dx}{dt}=1-4t+e^t Homework Equations None really. The Attempt at a Solution I know that a complimentary solution is x=c_1+c_2e^{2t} But when I try to guess say: x_p=At+B+Ce^t and plug into the DE, I do not get...

Homework Statement I must solve x^2y''-2y=x. Homework Equations Not sure. Reduction of order maybe. The Attempt at a Solution I notice that y_1=x^2 is solution to the homogeneous DE x^2y''-2y=0. I propose another solution of the form y_2(x)=v(x)y_1(x). Plugging this y_2 and its...

Homework Statement Hi I am trying to solve problem 2.1 in these notes (it is on the very first page): http://qis.ucalgary.ca/quantech/673/notes/chapter_two.pdf . The problem tells me to show that the Fourier transform of P^{(2)} (t) = \varepsilon _0 \frac{1}{{(2\pi )^2 }}\int_{ - \infty...

Homework Statement I must solve yy''-(y')^2-6xy^2=0.Homework Equations Not sure.The Attempt at a Solution I reach something but this doesn't satisfy the original DE... Here is my work: I divide the DE by y^2 to get the new DE \frac{y''}{y}- \left ( \frac{y'}{y} \right ) ^2-6x=0. Now I notice...

Homework Statement find general solution of x2y''-xy'-3y=0 Homework Equations two solutions are given, y1=1/x and y2=x3 The Attempt at a Solution i think this is a reduction of order question? the only theory i can find in my text for second order DE relates to constant...

Homework Statement I have got the diff equ problem solved out to y(t)=Ce^-t*cos4t+Ce^-t*sin4tHomework Equations now I have to solve for the IVP and the values are y(0)=1, yprime(0)=-1The Attempt at a Solution I believe for the first part I just plug in the y(0)=1 which results in the e^-t...

Homework Statement Hello, My first post here I have a numerical problem for Matlab but I get stuck with the basic math... For a circuit I have three equations: 1.Inductance: L=Lo/(1+I^2) 2.Voltage over the inductance: V=L*dI/dt 3.Current over a condensator: I=-C*dV/dt...

I am trying to solve the following problem and am a bit lost so any advice would be welcomed. x'' = 2x' + x = 3cos2t + sin2t My understanding is that I need to find the general solution for the unforced equation and a particular solution of the above equation. When these are added together...

Hi all, I understand the basic concept of undetermined coefficients, but am a little lost when g(t) in the equation yll+p(t)yl+q(t)y=g(t) is a product of two functions. The specific problem I'm working on is as follows: yll-2yl-3y=-3te-t When I solve for the homogeneous set of solutions I...

Homework Statement So I'm trying to get a grip about those Green functions and how to aply them to solve differential equations. I've searched the forums and read the section on green's functions in my course book both once and twice, and I think I start to understand at least som of it...

I've been trying to solve this one for a while. My professor wasn't even sure how to do it. Any suggestions? y''+t*y+y*y'=sin(t)

Homework Statement Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions. Homework Equations The Attempt at a Solution

Homework Statement I haven't done this for several years and have forgotten. Kicking myself now over it since it looks like something so simple but i cannot figure it out... I need to break this second order ODE into a system of first order ODE's in matrix form to use within a crank...

Homework Statement Which of the following functions are soltuions of the differntial equation y''+y=sin(x)? a) y=cos(x) b) y=sin(x) c) y=1/2*xcos(x) d) y=1/2*x*sin(x) Homework Equations The Attempt at a Solution I'm kind of lost on how to solve this problem. I don't think...

Hi everyone, Homework Statement I shall find the solution for the following differential equation: y''(x)+2y'(x)+y(x)=x^{2}+3 Homework Equations - The Attempt at a Solution At first solved the homogenous equation and found the general solution for the homogenous as the...

I want to find the second order derivative for f(x,y),x(u,v),y(u,v), f depends on x and y, and x and y depends on u and v. I'm trying to find \frac{{\partial^2 f}}{{\partial v \partial u}}This is what I did: \frac{{\partial f}}{{\partial u}}=\frac{{\partial f}}{{\partial x}}\frac{{\partial...

Homework Statement find a particular solutions for the given differentiable equation. Homework Equations y''+5y'+6y=4-t^2 The Attempt at a Solution Because the right-hand side is a polynomial of degree 1, so I want to have a particular solution of the same form. It's like...

Homework Statement Suppose that you are given a set of observations (tk,yk), k = 1,...,M. You plot these points on a sheet & it seems that the relationship between (t,y) could be approximated with a second order polynomial. a) Write down the model in the form y = Ax + c. Specify the vectors...

So the question is y" - y' - 6y = e^-x + 12x, y(0)=1,y'(0)=-2 First I found the general solution which came out to be, Ae^3x + Be^-2x I then Substituted y=ae^-x + bx + c y'=-ae^-x + b y"=ae^-x Then I just compared the coefficients to get a=-1/4, B=-2 and C=-1/6 So I am getting y =...

Determine the general solution to the ODE: y'' + 2y' = 1 + xe-2x I know the solution will be of the form y = yh + yp. The homogeneous solution is y = c1 + c2e-2x. For the particular solution, I have been using the method of undetermined coefficients. c3e-2x won't work as it is not...

Homework Statement Uxx+Uyy-c^2*u=0 for -inf<x<inf y>0, subject to boundary conditions Uy(x,0)=f(x), u(x,y) bounded as x-> +/- inf or y -> inf Homework Equations Fourier transform greens function? The Attempt at a Solution I would think that I would have to go through two...

So I'm computing a second order Taylor series expansion on a function that has multiple variables. So far I have this I(x,y,t)=dI/dx(change in x)+dI/dy(change in y)+dI/dt(change in t)+2nd order terms Would it still be a better approximation than just he first order if I included some...

Homework Statement y'' + 3y' + 2y = 0, y(0) = 1, y'(0) = 0 Homework Equations Finite Difference Approximations: y'' = (y(ii+1) - 2y(ii) + y(ii-1))/h^2 y' = (y(ii+1) - y(ii-1))/(2h) where h is the finite difference. The Attempt at a Solution I wrote the MATLAB code (just to try...

Homework Statement Solve: xy''+2y'=12x^{2} with u=y' Homework Equations if you have: y'+P(x)y=Q(x) then your integrating factor is: I(x)=e^{\int P(x) dx} The Attempt at a Solution The only reason I was able to solve this is because I stumbled upon a...

Homework Statement Consider the ODE: y''+p(x)y'+q(x)y=g(x) It is given that the functions y=x^{2}, y=x and y\equiv1 are solutions of the equation. Find the general solution of the equation. Homework Equations The Attempt at a Solution Well, given the three solutions, and...