Second order Definition and 570 Threads

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 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 +...

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 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...

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 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...

http://www.math.northwestern.edu/~clark/285/2006-07/handouts/lin-constraint.pdf It's actually proof of finding sign definiteness of quadratic form with linear constraints with sign of submatrices of bordered hessian. The proof is from page 2~page 3. I have 2 questions: 1. From about...

Homework Statement http://img534.imageshack.us/img534/9687/rlc.png Cannot do this question, the first part confuses me when it asks to find an equivalent Parallel circuit. My first instinct was to try to add the capacitor and inductor and 40k Resistance together to create an RLC series...

hello, I have read in a number of papers that if we have a cantilever beam and are only interested in the movement of the tip when the base is being excited at the frequency of the first eigen mode , then the whole beam can be replaced by a spring mass system. Can anyone tell me of a...

Solving second order linear homogeneous differential equation! HELP!? Solve the second order linear homogeneous differential equation with constant coefficients by reqriting as a system of two first order linear differential equations. Show that the coefficient matrix is not similar to the...

Homework Statement Let X(t), -inf< t < inf, be a second order process. Show that it is a second order stationary process if and only if mu(t) sub x is independent of t and r(s,r) sub x depends only on the difference between s and t. Show that is a second order stationary process if and...

Homework Statement This question concerns the second-order differential equation dy^2/dx^2 -4(dy/dx) + 5y = 25x - 3e^2x. Find the solution of the differential equation that satisfies the initial conditions y=0 and dy/dx= 0 when x=0. Homework Equations The Attempt at a Solution

hi. I can't figure out this question: d2y/dx2 - 2 dy/dx - 3y = x (i) find complementary function (ii) find particular integral (iii) using (i) and (ii) find the general solution (iv) find the solution that satisfies the initial conditions: y=2/9 at x=0 and dy/dx=-13/3 at x=0 i...

Hi. I have to solve this: y''-3y'+2y=e^x, Using the replacement y=\phi y_1 being y_1 a solution of the homogeneous differential equation. I can't do it "traditionally", I have to use this method. So I have to solve that \phi ''y_1+ \phi ' \left[2y_1'+Py_1] \right]=e^x So, this is what I...

Hi there. I had some trouble trying to solve this: y''+y=\cos x +3\sin 2x (1) At first I just found the solution for the homogeneous equation: y_h=e^{\lambda x} \rightarrow \lambda^2+1=0 \rightarrow \lambda_1,\lambda_2=\pm i Then y_h=C_1\cos x+ C_2 \sin x So I've tried to find the particular...

Homework Statement I have this problem, which says: If the graph of one solution for the equation y''+P(x)y'+Q(x)y=0 is tangent to the x-axis in some point of an interval [a,b], then that solution must be identically zero. Why? I've tried to do something with the general expression for the...

I am doing a spring mass problem. Unfortunately, I'm not proficient in Tex so this won't be as neat as it could be. Data: m1=1, m2=1; k1=0, k2=2, k3=0 Stiffness matrix: -(k1+k2) k2 k2 -(k2+k3) 1 0 * x1'' -2 2 * x1 0 1 x2'' = 2 -2 x2 From that, I...

Homework Statement I'm trying to solve a second order ODE for y(x) to show that the solution is y(x)=sin(x)/x. We've been told to use the substitution y(x)=h(x)/x. I've got to the stage of solving for h(x), arriving at h''(x)=-x. Using the general solution, h(x)=A sin(x) + B cos(x) and...

We are doing mass spring problems that stem from second order ODE's. I think my lack of linear algebra is hurting me once again in this section so any help would be greatly appreciated. We are using a stiffness matrix of K = [ -(k1+k2), k2 (row 2) k2, -(k2+k3)] Our first problem has the...

Dear All I'm stuck on something that seems to be contradictory. I was under the impression that the further the 2 closed loop poles are in a 2nd order system to the left of the root locus, the higher the damping. Surely high damping means longer rise time? But other sources say that the...

Homework Statement I'm given two equations first (d^2)*r/dt^2 - r((d*theta/dt)^2)= (-A)/r^2 --- this is a non linear second order differential equation second (r^2)*((d*theta)/dt)=B B and A are...

Homework Statement Solve the following second order linear differential equation d2x/dt2 + x = 2 cos(t) subject to the initial condition x(0) = 0 and dx/dt (0) = 0. What type of motion do you find? Homework Equations The Attempt at a Solution I don't know where to start

Homework Statement Given a second order differential equation: y'' + P(x)y' + Q(x)y = 0 If y1(x) and y2(x) are linearly independent solutions of the DE, what form does Abel's Equation give for W(y1(x), y2(x))? If we assume that one solution y1(x) is known, what first order DE results from a...

Homework Statement http://www.math.wvu.edu/~hjlai/Teaching/Tip-Pdf/Tip3-27.pdf Example 7. Not this question in particular, but it shows what I'm talking about. I understand how they get the first partial derivative, but I'm completely lost as how to take a second one. I have tried...