Second order ode Definition and 85 Threads

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?

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

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...

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 =...

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...

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...

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 A particular solution of y'' + 4y = tanx Answer choices are: (a) 1/2*cos(2x)ln|sec(2x)+tan(2x)| (b) -1/2*cos(2x)ln|sec(2x)+tan(2x)| (c) 1/2*sin(2x)(ln*cos(x)+x*sec(2x)) (d) 1/2*sin(2x)(ln*cos(x)-x*sec(2x)) (e) none of the above Homework Equations The...

Homework Statement What is the value of a such that the solution of the initial-value problem satisfies limx->infinity y(x) = 0? y''+y'=e^(-x), y(0)=1, y'(0)=a Homework Equations The Attempt at a Solution Not sure what to do with the missing y term... yp=Ae^(-x), y'p=-A^(-x), y''p=A^(-x)...

Homework Statement Solve ODE of form y''+(2/x)y'=C*(e^y) where C is a constant Homework Equations The Attempt at a Solution I don't really see how to approach this one, so a point in the right direction would be great. Thanks,

Hi I need to find the solution of d^2y/dx^2 + 2x(dy/dx) = 0 I've solved it in Maple and get that y=a*erf(x)+b but I have no idea how to arrive at this answer! Any help would be great, thanks.

Homework Statement Find the general solution to x'' + e^(-2t)x = 0, where '' = d2/dt2 Homework Equations - The Attempt at a Solution First I did a change of variables: Let u = e^(-t) Then du/dt = -e^(-t) dx/dt = dx/du*du/dt = -e^(-t)*dx/du d2x/dt2 = d/du(dx/dt)du/dt =...

Homework Statement y''(x-1)-xy'+y=x2-2x+1 The Attempt at a Solution I don't even know how to start this, Don't know what substitution to do.

Could you please help me or give me any hint to solve this ODE.. \frac{d^2y}{d x^2} + ( 2\rm{sech}^2 x - a^2 ) y = 0 where a is a constant. I want only even function solution. (y(x) = y(-x)) BTW, this is a homework problem. I encountered this equation while considering surface waves...

Hi guy, I have this ODE that I'm having problems with y"+4y'+4y= e^(-2x)logx Now, Using method of UC to get rid of the RHS I've tried using Ae^(-2x) x^2 logx However, I'm not quite sure whether that is correct or not as I have never had a question containing logs before

Ly ≡ (x +1)^2y′′− 4(x +1)y′+6y =0 given y[1]=(x+1)^2 is a solution, use the ansatz y2(x)= u(x)(x+1)2 to reduce the order of the differential equation and find a second independent solution y2 how to reduce !? and i can't find u ...can't solve (x+1)^2u''+6u=0 please help! thx!

Homework Statement It will be great if someone could show me some options: I need to prove the following: A particle of mass m is attracted toward a fixed point O (the origin) with a force proportional to its instantaneous distance from O raised to a positive integer power, i.e...

Find k: 20\frac{d^2x}{dt^2} + \frac{dx}{dt} + kx = 0 when t = 0 - x = 1 - dx/dt = 1 My attempt at this in maxima: (%i1) 20*'diff( 'diff(x, t), t) + 'diff(x, t) + k*x = 0; 2 d x dx (%o1) 20 --- + -- +...

Hi All, I was looking for the general solution of an equation as y(x)'' = f (y), and found the attached document on the web. It presents the solution in a way which I am not sure I understand. I tried to look at the trivila example y'' = - y, solution y = sin (x), but I am struggling in...

Homework Statement Question and part 1 as above. The second part involves solving this equation where L = 8R^2 C. The system is kept in steady state by maintaining V(t) = -Q/C (constant). V(t) is then set to 0 at t=0. It also says "Note that V(t)=0 for t>0 and that appropriate initial...

Homework Statement find the general solution to the ODE: y''+(1/x)y'=0 Homework Equations The Attempt at a Solution I put this in the following form: y''=-(1/x)y' integrated both sides: y'=-ln(x)y +C I think i made a stupid mistake but i can't figure out what it is. Any help...

Homework Statement Find the general solution of the following diff. eqn. y''(t) + 4y'(t) + 4y(t) = t^(-2)*e^(-2t) where t>0 Homework Equations General soln - Φgeneral(t) + Φparticular(t) Wronskian - Φ1(t)Φ22'(t) - Φ2(t)Φ1'(t) The Attempt at a Solution I'm solving by...

second order ODE solution for this system?? hello guys, I am wondering if what is the analytical solution for this system? can we solve it as a mass-spring-damper system? thanks for your helps. the rectangular part is removed from the disk. http://img3.imageshack.us/img3/3610/odev.th.jpg

Little homework problem that I'm beating myself up over... Solve: xy'' - 2y' + xy = -2\cos x Using the method of Laplace transforms... So I do some jiggling and get to: (1+s^{2})\frac{dF}{ds}+4sF(s) = \frac{2s}{s^{2} + 1} To which I find the following solution: F(s) =...

Hi all, My maths are very rusty and I would need some advice. I have some experimental results obtained in an open channel and got depth-averaged velocity u(y) at different cross-sectional locations y. I tried different models but there is one I don't know how to tackle. The following one...

Can someone explain to me why the solution of \frac{d^{2}\Phi (\phi)}{d\phi^{2}} = -m_{l}^{2} is \Phi = e^{im_{l}\phi}?

The Problem You are given: http://img530.imageshack.us/img530/4468/88346476ca9.jpg Where http://img408.imageshack.us/img408/209/53113174nt5.jpg is constant (taken as B). a) Differentiate both sides to produce a second order ODE for y(x) b) Show that it can be written as a first order ODE...

Hi, I am trying to decide whether y(t) = c1t^2 + c2 t^−1, where c1 and c2 are arbitrary constants, is the general solution of the differential equation (t^2)y'' − 2y = 0 for t > 0 and justify the answer, but I don't really know how to approach it from this "side" of the problem. Any suggestions...

Solve the initial value problem y''+3y'+2y = 3e^{2t}+1 with initial values y(0) = 1, y'(0) = 1. I am unsure if I am going about the solution correctly. 1.) Find the characteristic equation. r^{2}+3r+2=0 \Rightarrow (r + 1)(r + 2) = 0 Therefore, y = c1•e^{-t}+c2•e^{-2t} 2.) Use method of...

I am having a problem coding a Matlab code that solves a second ODE equation which I give below: x^3*(1-2*x*M)d^2J(x)/dx^2+2*(2*x^2+i*nu*x-7*x^3*M)*dJ(x)/dx -2*(2*x+8*M*x^2+i*nu)*J(x)=0. where M = 1 (Mass of a black hole), nu = 0.74734+0.17792*i, J is a function of x, i represents a complex...

Regarding: (a+bx+cx^2)y^{''}+(f+gx+hx^2)y^{'}+(j+kx+mx^2)y=0 Does anyone here know if it's been "completely" characterized in terms of the geometry of the three parabolas which make up it's coefficients? For example, if I'm given plots of the parabolas, can any information at all be...

Assume the next differential LINEAR second order equation: w''+\frac{4}{x}w'+\frac{4}{x^4}w=0 So I thought: OK, I need two independent solutions w_1 and w_2, because the space of solutions is of dimension two. Then the professor gave us a solution: w=sen(2/x)-(2/x)cos(2/x) and I...

Suppose we have y'' = f(t, y); y(a) = y0; y'(a) = y0' Note all derivatives are with respect to t. Let u = y', then u' = y'' 1. u' = f(t, y), u(a) = y'(a) 2. y' = u, y(a) = y0 Question 1: For y' = u, should I think of this as dy/du = u? Otherwise, I don't see how to solve 2 because...

How would I go about finding a solution to this differential equation? r\ddot\theta-g\sin\theta=0 Where r and g are constants.