2nd order Definition and 494 Threads

Homework Statement obtain the general solution y(x) of y''-2y'+y=e^(2x)/(e^x+1)^2 Homework Equations variation of parameters The Attempt at a Solution I have obtained the continuous equation. I tried two methods of variation of parameters, but both of them got me stuck. 1...

u'u''-k1u=-a*cos(hy)-b where,u'=du/dy; and and a,b,k1 are constants conditions u(-H)=0; u'(0)=0; where 2H is height of the channel where the liquid is flowing please help any suggestions are welcome i couldn't find the analytical soln numerical soln also am havin a dead end so please

Hi, I am looking at the following 2nd order DE with variable coefficient: y''(x)-(1/x+7)y(x)=0 I would be grateful for any help in regard to methods which may be applied to such an equation. Many thanks in advance! C.

Hi I am trying to solve an analytical solution for a single-DOF system with a non-linear damping component: mx'' + B2x'x' + B1x' + Kx = 0. Tried in maple with no success with the non-linear term in the eqn. Thanks in advance.

Homework Statement the problem is to solve this differential equation: x^2 y'' + xy' + (4x^2 - 1)y = 0

Hey guys! I'm trying to solve a 2nd order differential equation. I am quite familiar with the method of solving these equations like treat them like characteristic equation ODE. but there's a question which I really want to solve. question is d^2 X/dt^2 +dX/dt +sinX=0. How should I solve this??

So I've been trying to figure this out for a while now and all my attempts have failed, like I tried using the command ODE45 but it did not work... this is the equation -> m(d^2x/dt^2) = −kx − β(dx/dt) I'm given that 2λ = β/m, and and ω^2 = k/m and I must solve for when λ^2 − ω^2 > 0 I...

Hi, This is from "3000 solved problems in physics". Yes, I have the solution but I still have a question. a ball is thrown vertically upward with a velocity of 20 m/s from a top of a tower having height of 50m. On its return it misses the tower and finally hits the ground. What time t elapses...

Hello, I've started learning how to numerically integrate ODE's and I've run aground when i posed a 2nd order system for mathematica. Here is my initial code: NDSolve = [{x'[t] == -y[t] - x[t]^2, y'[t]==x[t], x[0]==1, y[0]==0.5},{x,y},{t,0,30}] and i get an error message saying the...

Homework Statement Find the general solution to the differential equation \frac{d^2y}{dx^2} -2*\frac{dy}{dx} +2y =g(x) where g(x) = −14 cos(2x) − 2 sin(2x) Homework Equations The Attempt at a Solution ive found the homogenous solution which is y=e^x (ae^ix +be^-ix) what I...

Homework Statement The equation t^2y'' + 4ty' -4y = 0 has a solution of y(t) = t. Find a second, linearly independent solution. 2. The attempt at a solution Ok so I just applied the Cauchy Euler equation method to find a general solution of y = c1*t^-4 + c2*t Where c1 and...

Hi guys have a big problem trying to find the unique solution to the 2nd order diff equation shown below: y’’(x) = 2xy’(x) + 4y(x) where y(0) = y’(0) = 1

Homework Statement Need to solve for dx/ds in the following equation, keeping dy/ds. Homework Equations d^2x/ds^2 - (2/y)(dx/ds)(dy/ds) = 0 The Attempt at a Solution I can just rearrange to get: dx/ds = (y/2)(ds/dy)(d^2x/ds^2) But, this is not clean to use for some later...

Homework Statement There's a catalyst pellet in a reactor and I'm supposed to prove an equation for the maximum temperature which is: Tmax=Ts +[(-H)*(D*Cas)]/k Tmax= max temp, Ts = temp at catalyst surface, T=temperature, H=enthalpy of rxn, D=diffusivity, Cas= concentration at...

There's a catalyst pellet in a reactor and I'm supposed to prove an equation for the maximum temperature which is: Tmax=Ts +[(-H)*(D*Cas)]/k First thing I did was develop an Energy Balance across the spherical catalyst and I got the following equation: (1/r^2)*d/dr(r^2*k*dT/dr) +...

Hi all, I was looking at the buckling problem of a piece of paper with both ends clamped. When the two ends come closes they form a bulb-like shape and I was interested in deriving the shape numerically by solving NL ODE, which comes from energy methods (neglecting gravity). The ODE I got...

So I was trying a few quantum mechanics problems and encountered this diff eq: \frac{\hbar^2}{2m}\frac{\partial^2}{\partialx^2}\psi(x) + \frac{1}{2}kx^2\psi(x) = E\psi(x) I put it into the form: \frac{\partial^2}{\partialx^2}\psi(x) + (\frac{2mE}{\hbar^2} - \frac{m}{\hbar^2}kx^2)\psi(x) = 0...

Find the general solution of x2y'' + xy' + (x2 - 1/4)y = 0 and express it in terms of trigonometric functions. (You don't actually have to solve the equation from a trial function in this problem, but you must identify the differential equation. Then, you may write the solution and prove...

Homework Statement Find the general solution of the following differential equation: y" + 3y' + 2y = sin ex Homework Equations y = yh + yp homogeneous solution: (found by solving characteristic eq) yh = Ae-2x + Be^-x The Attempt at a Solution from my table if r(x) = ksin(wx)...

Equations: (d^2r/dt^2) - r*(dθ/dt)^2 = -10/(r^2) and r^2*(dθ/dt)=1 How would I get three 1st order ODE's from this?

hi i am trying to solve second order ODE in MATLAB but when i write my scribt and call into the command window using ode45 i get input argument "a" is undefined i have spent so much time trying to figure out what the problem is but unsuccessful. the function is as follows function...

Homework Statement x^2 y''+2xy'-12y=0,y_1=x^3 y''+(2y')/x-12y/x^2 =0 Homework Equations The Attempt at a Solution y=uy_1=ux y'=u' x+u y''=u'' x+2u' subbing that in instead of y,y',y'' u'' x+2u'+2(u'x+u)/x+12(ux)/x^2 =0 now my book says to reduce the...

Hi, could anyone give me a hint on what method to use to solve this ODE: v''+(2/t)v'+(b)v=0, b is a constant and v=v(t). Most of my ODE training resolves around how to solve the above equation with constant coefficients. AND all of my reference books say that "the nonconstant case is...

Homework Statement Ive been told to perform 2-3 Picard Iterations on the following problem Homework Equations y'' = 6y^2 With initial conditions: y(0) = 0 y'(0)= -2 The Attempt at a Solution In class we've gone through how to perform picard iterations and it has been easy so far...

Homework Statement y''-3y'=4 Homework Equations none The Attempt at a Solution I've been looking at this problem for the last hour and have absolutely no idea on how to solve it. My initial approach is this: y''-3y'=4 therefore r^2-3r=0 so r =0,~3 giving a...

Homework Statement y''-3y'+2y=t e^{2t}+sin(5t) Homework Equations The Attempt at a Solution I can get as far as this: y_h(t)=c_1 e^{2t} + c_2 e^{t} y_p(t)=At e^{2t} + B e^{2t} + C sin(5t) + D cos(5t) My professor says we multiply At e^{2t} + B e^{2t} by t to give At^2...

I've written a program to show the trajectory of a rocket around the Earth with initial conditions that can be manipulated to fix a circular or elliptical orbit. We start with Newton's 2nd law and use the equation a=F/m in freespace (so m can divide out) to get a 2nd order ODE and solve by...

Question: Find the real-valued general solution of the differential equation y''+1y'+1y=0 where primes indicate differentiation with respect to x. (Use the parameters a, b, etc., for undetermined constants in your solution.) My attempt: Use characteristic equation: r^2+r+1=0 I used the...

Homework Statement \epsilony'' - y' = 0 y(0)=0, y(1)= 1 The Attempt at a Solution this s a perturbation problem, but I'm not sure how to go about doing it if we let epsilon = 0 we'll go from 2nd order to first order so it's a boundary layer problem... i think so if that's the...

question concerning basic Diff.Eq. 2nd order "trick" Homework Statement First of all, this is NOT for homework. In fact, this is a conceptual question. Now then, let me address my problem by presenting a simple example. Let's say you have a second order equation with initial conditions...

x y'' + (x + 1) y' = 2 x Solve for y(x). Due to the coefficients being a function of x, I have no idea where to start to find the homogenous solution (Complementary Function). I know how to proceed after this part with the variation of parameters method. I just have no idea where to...

Homework Statement y'' = t^2 The Attempt at a Solution The general solution to the homogenous diff equation is y(t)= C1 + tC2 i beliee. The particular solution is where i am having trouble. the guess is of the form \alpha t^2 + \beta t + \gamma ... but taking 2 deriatives leads to...

Homework Statement The solution to the initial value problem x y''(x) + 2y'(x) + xy(x) = 0; y(0)=1, y(0)=0 has derivatives of all orders at x=0 (although this is far from obvious). Use L'Hopitals rule to compute the taylor polynomial of degree 2 approximating this solution. Homework...

Homework Statement Argue that if y=f(x) is a solution to the DE: y'' + p(x) y' + q(x) y = g(x) on the interval (a,b), where p, q, and g are each twice-differentiable, the the fourth derivative of f(x) exists on (a,b). Homework Equations The Attempt at a Solution Its a general...

I have a 2nd order system response on a graph. How would I go about this to develop the equation that models this system in s- domain when its graphed in time domain like I have ?

http://img213.imageshack.us/img213/7402/30788730.jpg This questions consists of a total of 13 marks - 6 marks for the first order DE - 7 marks for the second order DE I attempted the solution as below. I could solve the second order DE using normal method but when I think again the word...

Homework Statement The system's closed loop transfer function is given below, find K and \alpha such that the input R(s) = 1/s^2 has no steady state error. (Hint: the system is not a unit feedback system) http://img829.imageshack.us/img829/9899/problempr.png Homework Equations not sure...

Hi all, I am having a hard time solving a partial second order differential equation with an imaginary part. I basically took a much bigger function with real and imaginary parts and simplified it down to this. I also know the solution to a similar equation (shown in image). Any help would...

i managed to get the indicial equation/recurrence relation, but for parts (a) and (b), I am stuck. i got a0,a1,a2,a3... for part b, but how do i get the polynomial solution? Thanks!

I can not how define way to solve these equation x(l-x)y''+4y'+2y=o If anyone can help

I seem to get the correct answer, but when i check my answer on wolfram, there is a 3C(2) instead of just C(2), am I doing something wrong or it doesn't matter if it is a 3C or C?

http://www.ece.ubc.ca/~shahriar/eece251_notes/eece251_assignment6.pdf Question 4 on the link. I understand why the top inductor to the left has i = 0A but I don't understand why it has a voltage of 3.816V, can anyone care to explain?

Some one please help me how to prove the following: \dot{A}:B + A:\dot{B}=A^{\nabla J}:B+A:B^{\nabla J} A and B are II order tensors and : represents the inner product.

http://www.ece.ubc.ca/~shahriar/eece251_notes/eece251_assignment7.pdf Hey guys, I have a question about my 2nd order circuit assignment. I posted the link to my assignment, and the question I have is question 2. I know that the question saids its a capactior and the circuit diagram itself has...

Hi all, I have a 2nd order ODE I am trying to solve using NDSolve. In the ODE there are two constant coefficients and an initial condition that I want to 'vary'; meaning, I have a table of initial conditions with corresponding constant coefficients. It is straight forward to solve the ODE...

Homework Statement (tw')' + tw = 0 with w(0) = 1, w'(0) = 0 on the interval [0,1] by introducing the new variable v=tw' and considering the resulting first order differential system involving w and v Report your computed solution (wh(1),vh(1)) for h=1/10. Homework Equations The...

The formula given by my instructor for a Taylor Series approximation of the second order at point (a,b) is f(a,b) + grad(f(a,b))x + 1/2 H(f(a,b)) x If you recognize this formula, do you know what the x vector is? Note: x is the x-vector, and H represents the Hessian Matrix. Thanks! The...

Homework Statement y'' + y = -2 Sinx Homework Equations The Attempt at a Solution finding the homogeneous solution, is simple; yh(x) = C1 Cos(x) + C2 Sin(x) for the particular solution, I let y = A Cos(x) + B Sin(x) thus, y' = -A Sin(x) + B Cos(x) y'' = -A Cos(x) - B...

Homework Statement Hi everyone, I'm a bit stuck and have been staring at my fortran code all day. For my project this year I'm writing a program to model a spiral galaxy in which gas clouds circulate, collide and produce star formation. I've written code for gravitational acceleration due to...

Homework Statement t''[x] = \frac{2}{t} t'[x]^{2} The Attempt at a Solution This is not your basic 2ODE, since I can't separate the components into y'', y' and y. Help? I've so far tried: \frac{d^{2}t}{dx^{2}}=\frac{2}{t}(\frac{dt}{dx})^{2} \frac{dt}{dx}=\frac{2}{t}(\frac{dt}{dx})^{2}dx...