Second order Definition and 602 Threads

Homework Statement Find if it is true that the general solution to : y'' - y' = 0, where y(x), can be written as : y(x) = c1 cosh(x) + c2 sinh(x), where c1 and c2 are real arbitrary constants. Homework Equations differential equation solving The Attempt at a Solution I just...

Homework Statement I have differential equation;] this is equation from central force thing in Lagrange mechanics, you know, you know, its second order hahaha:D y^3y^{\prime\prime}=ay+b Homework Equations I will using method of making a first degree of this equation The Attempt at a...

Homework Statement from one thing in Lagrange mechanics (general coordinates: \phi,\dot\phi,s,\dot{s}) I got a equation system: \begin{cases}R\ddot\phi\sin\phi+R\dot\phi^2\cos\phi+\ddot{s}=0\\ g\sin\phi+R\ddot\phi+\ddot{s}\sin\phi=0\end{cases} The Attempt at a Solution Is it good idea to...

Hi guys, I really have no idea how to approach finding the particular integral for, say: f'' + 5f' + f= e^x sinx Could anyone help me? And for future reference how do you go about finding the PI for any combination of polynomials/exponentials/sinusoidals? Thanks in advance for the help!

Hi, i have the following non-homo differential equation. y^{\prime\prime}+4y = 2~cos~x + 3x~sin~x \begin{cases} y(0) = 1 \\ y^{\prime}(0) = 2 \end{cases} Since there is a 3x term in front of sin x. What is the form of the solution for this problem? if it hadn't been there it...

Is there any physical reason why second order approximation to ground state in time independent perturbation theory is always negative. I know how to prove it mathematicly but I wonder whether one may justify it using only physical arguments.

Hello, I hope I am writing to right part of a forum... I made a differential equation when I was solving my problem, but unfortunately I am not capable of solving such equation since I am only 12th grader. Or maybe it is not possible to solve it at all...

How do i solve the following equation? u= L*(d^2i/dt)+ (1/c)*i r* (di/dt)L= 1,4 mF C= 0,31 H R= 1000 ohm Well i have so far found the auxiliary equation: 0,31*r^2 + 1000*r + 1/(1,4*10^-6)=0 And the discriminant is found to be 114286. This makes the form of the solution: Y=c1*e^r1x +...

I've created a second order homogeneous equation from my orginal data m(d^2x/dt^2) + kx = 0 how can I turn it into a expression of displacement relevant to time?

Homework Statement I have a RLC circuit in series. I am trying to find the current i(t) passing through this RCL circuit. When solving the RCL circuit, it happened to be critically damped. And simplified i ended up with: i(t) = A2te-20t Where i need to find what is the cosntant A2 Homework...

Homework Statement a and b are functions of z: a=a(z); b=b(z) I want to calculate the second order partial derivative operator on z Homework Equations Using the chain rule: \frac{\partial}{\partial z}=\frac{\partial a}{\partial z}\frac{\partial}{\partial a}+\frac{\partial...

Homework Statement Find a third degree polynomial approximation for the general solution to the differential equation: \frac{d^{2}y}{dt^{2}} +3\frac{dy}{dt}+2y= ln(t+1) Homework Equations Power series expansion for ln(t+1) The Attempt at a Solution The system to the...

Homework Statement Consider the differential equation \bold{x}'=\left[ \begin{array}{cc} -1 & 2 \\ -1 & -3 \end{array} \right]\bold{x}, with \bold{x}(0)=\left[ \begin{array}{c} 1 \\ 1 \end{array} \right] Solve the differential equation where \bold{x}=\left[ \begin{array}{c} x(t) \\ y(t)...

I understand how to solve a normal second order linear equation, but this question in the homework is a bit more theoretical and I'm a bit confused. "Suppose y1(t) and y2(t) are solutions of y'' + py' + qy = 0 Verify that y(t) = k1y1(t) + k2y2(t) is also a solution for any choice of...

Hello sorry for my English, i know its bad;) I have a simultaneous differential equation of second order (moving of point mass around point mass M in beginning of cartesian system) \begin{cases}\frac{\mbox{d}^2x}{\mbox{d}t^2}=-GMx\left(x^2+y^2\right)^{-\frac{3}{2}}\\...

For my thesis I need to solve many differential equations non linear, second order by using maple... For example figure adjoint using dsolve command, the solutions are very extensives and very bad. there is a suggest for to solve the differential equations by using maple? there is some...

A Nonlinear Second Order Differential Equation Problem: very frustrating please help! Hello, I am a first year engineering undergraduate student, and this is my question. Homework Statement A dust particle of negligible mass starts to fall, t=0, under the influence of gravitational force...

Hi, I came across the following differential equation: \sqrt{1+(y')^2}=\frac{d}{dx}\left(y\frac{y'}{\sqrt{1+(y')^2}}\right) I found possible solutions: y\left(x\right)=cosh(x+C_{1}). However, this is a second order ODE so there exist a more general solution, with 2 freedom degrees...

hello i need some help here! solve: x''+3x'+2x=1/(1+e^t) well ok the homogeneous solution is c1*e^t+c2*e^2t but how to determine the particular solution Xp!

Okay, so my problem lies within taking the second derivative of a change of variable equation. w = f(x,y); x = u + v, y = u - v so far I have the first derivative: dw/dx = (dw/dv)(dv/dx) + (dw/du)(du/dx) = (d/dv + d/du)w Now I'm having problems in finding my second derivative...

Homework Statement Find the general solution to y'' + y = sec3(x) The Attempt at a Solution Well I can get the characteristic equation: r2 + 1 = 0 r = +-i Then the homogeneous solution is yh = C1excos(x) + C2exsin(x) And I know y = yh + yp but how do I get yp? I've never...

Hi everyone, I am studying to write my final Mechanical Engineering Prep Exam and have come across some problems that I am having a hard time figuring out. I have managed to figure out how to use the Euler-Cauchy Equations to solve problems of the form: x2y" + axy' + by = 0 where a and b...

Just wondering does it matter which coupled differential equation you solve first ( i terms of time)? normally i just solve the first equation, so far all our tutorial question involved finding solutions to second order equations that have 2 distinct roots ( for the auxilliary equation)...

Hi, I have a second order differential equation but I do not know how to solve it. \frac{d^2Q}{dn^2}\left -A(B-n\right)\frac{dQ}{dn}+ \left(A + \frac{C}{n}\right)Q = 0 Appreciate if anyone could help me on this. Thank you

Hey Guys, I've been banging my head with this one for a few days now. I've done (a) and (b) but I'm yet to do (c) if someone could complete this for me or help me along the way that would be greatly appreciated. Thanks heaps!

When we write down a Lagragian for a quantum field theory, it is said that it should not depend on the second and higher order time and space derivatives of \phi, because we want the equation of motion(EOM) to be at most second order. Why is it so important. What trouble will a higher order EOM...

hi, everybody i got for homework a pendulum on a cart. i solved the system and got two equations. (m+M)x'' + M L theta'' = F x'' + L theta'' + g* theta = 0 F = 1000 N, m = 500 kg, M = 1250 kg, l = 10m i know how to put them in state space and solve them with SS block in...

I think I know how to solve \frac{d\vec{x}}{dt}= A \vec{x} where A is a constant nXn matrix. We just compute the eigenvalues and the corresponding eigenvectors. But how do we solve \frac{d^2\vec{x}}{dt^2}= A \vec{x} Can we say straight away that the solution is...

Homework Statement find the general solution to the second order ode: x4y''+2x3y'+y=0 Homework Equations using Euler's method The Attempt at a Solution assume that the solution is y=xa then y'=axa-1 and y''-a(a-1)xa-2 substituting these into the ode: a(a-1)xa+2axa+xax-2=0...

Homework Statement Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 1.99 m away. If the first-order maxima are separated by 1.36 m on the screen, what is the distance between the two second-order maxima? Homework Equations I think these...

Dear Friends i am lookin g for the solution for second order differential equation. will anyone please help me to solve this problem.

Homework Statement I'm not sure if this is actually solvable, or a typo on my homework... but here's the problem in question: Solve the ODE: \frac{d^{2}y}{dt^{2}} + t^{2} \frac{dy}{dt} + y^{2} = 0, y(0)=0, y'(0)=0Attempt at solution I've been stumped on where to even start with this one, but...

I am not able to find the general integral of the following non-linear 2nd order equation: y^2 y'' + a y^3 - b = 0 in which: y = f(x) 0 < a <= 1, is a constant b > 0 , is a constant.

Hi I'v got a maths exam on Tuesday for my 2nd year of chemial engineering. Been going through a past paper and have been going over 2nd order homogenous DE's Im at the stage of calculating the roots (wether repeated or 2 distinct roots) I take the easy path like so: E.g m2 + 4m + 4 =...

Homework Statement Suppose that L is a second order linear differential operator over the interval J, that f is a function defined on J, and that the function v has the property that Lv = f on J (a) Show that if y = u + v and that Lu = 0 on J, then Ly = f on J (b) Show that if Ly = f on...

Homework Statement 4xy'' + 2y' + y = 0 2. The attempt at a solution In class, we were given that y1 = c1Cos(\sqrt{}x). We then used reduction of order to figure out the other solution Yet, I've been trying to figure out, is how do you get y1 in the first place? To me, it doesn't...

I hope this is the right place to post this question. I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C. I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative...

Homework Statement y''+16y=9xe^(4x) y(0)=0 y'(0)=0 find the solution, y(x) to the differential equation The Attempt at a Solution I found the particular solution to the right side of the equation, which is correct, yp= .28125x-.0703125e^(4x) For the left hand side of the...

Can anyone help me to solve the following second order linear 'ODE' for V(x,s,t): \frac{\partial^2 V(x,s,t)}{\partial s^2} = g(s) V(x,s,t) where g(s)=\frac{a^2}{B^4}+\frac{s^2 w^2}{B^2}. Here, a, b and w are (real) constants.

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...

Hey everyone, I've been doing some experiments with analog computers to further my knowledge of op-amps (and second order differential equations!) This is more of a mathematical question than an electrical engineering question, so I thought I'd ask it in this section. I'm looking for some...

Terms of "second order" and "fourth order"...what does this MEAN?! I am reading the paper written by Born and Oppenheimer that explains the development of the Born-Oppenheimer approximation. The paper contains the following cryptic (to me) statement: "The nuclear vibrations correspond to terms...

I would very much appreciate if anyone can help me with this problem. I got stuck at the end. I have to find 1.the complementary function, particular integral and the general solution. 2. find complete solution when t=0, q=0, dq/dt=0. -equation...

Hi all, For my thesis I would like to solve the following second order nonlinear PDE for V(x,\sigma,t): \frac{1}{2}\sigma^2\frac{\partial^2 V}{\partial x^2}+\frac{1}{2}B^2\frac{\partial^2 V}{\partial \sigma^2}+a\frac{\partial V}{\partial \sigma}=0, subject to the following boundary...

Homework Statement Solve the initial value problem y" = 2x - y' , y'(0) = 1 , y(0) = 0 I know this is probably a simple problem but I don't have a book for the class yet and the teacher didn't really cover this material in class but we still have homework due on monday so i need to figure...

Hello, I was wondering if I could get some help with a question I have. Homework Statement We are asked to find the first and second order partial derivatives of f(x,y) = x^2 - y^2 - 4x^2/(y - 1)^2 (sorry, I don't know how to write this in latex). I am not really sure how to get started...

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...

Top of page 69. I get six second order terms. Two of them cancel. Two are the ones on the right of 3.11. The other two involve KμKμ and KνKν. Why are there no such terms on the right of 3.11? I'm probably just missing something painfully obvious.

In my research, I'm using a modified version of the wave equation: \[ c^2 \left( {\frac{{\partial ^2 p}}{{\partial x^2 }} + \frac{{\partial ^2 p}}{{\partial y^2 }}} \right) = - \tau c^2 \left( {\frac{{\partial ^3 p}}{{\partial t\partial x^2 }} + \frac{{\partial ^3 p}}{{\partial...

How to prove that y''=d2y/dx2 if y=f(x)