2nd order Definition and 464 Threads

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...

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...

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 [SIZE="3"]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...

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...

Hi, have this strange 2nd order ODE in one of my tutorials that I am struggling to start. I am not used to dealing with derivatives of both x and y as well as a function involving t. I was wondering if anyone may be able to point me to the starting line. I am trying to convert them into 1st...

what's the method to solve a diff. equation as follows: d^2(psi)/d(x^2) - (k^2)*(psi) = 0

I'm working on a complex analysis problem from Arfken. Integrate[ (cos(b*x)-cos(a*x))/(x^2), {x, -Infinity, Infinity}] and show that it is equal to Pi*(a-b) Attempt: I first look at a related problem (or one that I think is related). => f(x) = sin(x)/x => f(z) = sin(z)/z...

Homework Statement A curved mirror of equation y=y(x) has that property that whenever a ray of light emanates from the origin it reflects parallel to the x-axis. Find the equation of the mirror Don't even know how to get started on this, Don't need a solution just need some starting hints...

Homework Statement y1 = x2 and y2 = x3 are two different solutions of x2y'' - 4xy' + 6y = 0, both satisfying the initial conditions y(0) = 0 = y'(0). Explain why these facts don't contradict Theorem 2 (with respect to the guaranteed uniqueness). Homework Equations The Attempt at a...

Homework Statement Find the particular solution of the linear, homogeneous, 2nd order differential equation: y'' - 2y' + 2y = 0, given the solutions y1 = (e^x)*(cos x), y2 = (e^x)*(sin x), y(0) = 0, y'(0) = 5. Homework Equations The Attempt at a Solution How do I begin? I'd really...

Homework Statement Verify that y1 = (e^x) * (cos x) solves the linear, homogeneous, 2nd order differential equation y'' - 2y' + 2y = 0 Homework Equations The Attempt at a Solution So I used the product rule but just kept going in circles with the cos x. I remember there's a way to...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

a\text{''}[t]+B[t]*a'[t]-A[t]*a[t]==0 a[0] = 10^-9 a'[0] = 0 a[t] = ? The coefficients A and B are variable over time. I HAVE solved (experimental and theoretical values) for the values of A and B over the time interval of interest! I attempted to solve for a[t] using NDSolve as one...

Homework Statement Find a value of the constant r such that both e^rt and te^rt are solutions to the ODE ay''+by'+cy=0 Homework Equations The Attempt at a Solution can anyone guide me with this question please. I am not sure where to start. I know that e^rt is always a solution...

Homework Statement y'' -2y' +5y =0 , y(0)=1, y'(0)=1 you get a complex root conjugate. Homework Equations y=e^(rt) y'=re^(rt) y''=r^2 * e^(rt) The Attempt at a Solution I have in my notes sin(omega*t)e^(sigma *t), cos(omega *t)e^(sigma). I don't think i took down the notes...

Hi, I've spent days trying to solve some equations in a paper (referenced below) that describes it as a "straightforward, albeit lengthy integration," but I can't work out the "straightforward" bit. The notation is also odd, which doesn't seem to help my problem. Perhaps someone could help...

Hello everybody, could you please direct me how to solve this nonlinear differential equation analytically, so by mathematica or matlab? I really need to solve it for my research project, so please help me du/dx=d/dx[a*u^(-1/2)*du/dx]-n*u^(3/2)*(u-c)/b boundry conditions are: u(0)=b+c...

Hi Guys, I know how to find the solution to a 2nd order homogeneous with constant coefficients but how do you solve one with a non constant ie x^2y''+2xy' ... etc = 0 Is there a general solution formula for these types of problems? My book seems to jump from 2nd order...

What does "to 2nd order" mean? http://www.mathpages.com/rr/s2-11/2-11.htm I thought "to second order" meant an approximation consisting of the initial terms of the Taylor series up to and including the second derivative term. For example, it seems to be used that way in the Wikipedia...

Homework Statement This was an example the teacher gave us to do in class. Unfortunately, I was a little behind on the notes so was not able to copy down the steps to solving this one. I did, however, get an answer problem: y'' + y = e^x + x^3, initial conditions y(0)=2, y'(0)=0...