2nd order Definition and 464 Threads

Hope I have posted this in the right section, this question is half differential equation and half finite difference method. The equation I have is a form of the Lucas Washburn equation, which is concerned with capillary rise...

I've recently been trying to solve the following equation: d2x/dt2 + (x2 - a) dx/dt + (x2 - b)x = 0 I've reduced it to a first order equation by a simple substitution of y = dx/dt to obtain: dy/dx = (a-x2) + [(b-x2)x]/y = 0 However I cannot figure out how to solve this equation. Is it...

Hi i need some help with solving this equation2 d2y/dt2 + dy/dt +10y = 3sin(9t) - 8e-2t - 7 when y=0 dy/dx = 10 t=0 The bit i am not sure about is the -8e-2t - 7 bit on the right side because i only know how to deal with 2nd order differential equations when they are of the form a d2y/dt2...

Homework Statement f"(t)-f'(t)-2f(t)=12H0(t-3), f(0)=f'(0)=0 relevant equations, are the laplace transform equations.. H0(t-a)=e-as/s The Attempt at a Solution LT:s2F(s)-sF(s)-2F(s)=12e-3s/s =>F(s)=12e-3s/s(s+1)(s-2) ok now from here, I am lost, i can't do partial fractions can I? and i need...

Homework Statement This is a problem from my book that I'm very close to finding the solution to, but I'm a little off. I have a feeling it's some small error I'm just overlooking because I'm so hungry/sleep-deprived. Anyway, the question asks you to find the Laplace transform of the given...

What are the commands to i find the peak time, seetling time, rise time and maximum overshoot of a second order system in matlab?

Hi, I have a second order differential equation with a solution in the form: f(t) = Ae^{t}+Bte^{t} I want to solve for t, ie. work out for what value of t does the function f(t) have a particular value. But there seems to be no way (that I know of) to do this. Can anyone give me any...

Homework Statement By using the method of undetermined coefficients,find the particular solution of y''+y'+y=(sin x)^2 Homework Equations i know how to determine the particular solution IF it is sin x. Ex: sin x ====> Asin x + B cos x (particular) but i wonder how to determine the...

While studying the Einstein Equation, I noticed something curious, at least to me with little experience in General Relativity. Start with the usual formulation of the equation: R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R + g_{\mu\nu}\Lambda = \frac{8{\pi}G}{c^2}T_{\mu\nu} Then, apply the...

I have the following equation subject to y(0)=0 and y'(0) = 0 my'' + b y' + k y = C I have done an experiment where I measured force at given depth for a dampened harmonic oscillator. Is it possible to use the force I measured to solve for displacement and then back out coefficient b for...

x''+x'+2x=0 x(0)=2 x'(0)=0 I've taken the characteristic equation and reduced the roots to 1/2 +- Sqrt(7/4)i of the form a +- bi (i = sqrt(-1) Then i put the homogeneous solution into the form of e^{}at*(B1cos(bt)+B2sin(bt)) for B1 i used the first i.c. and found that B1=2...

Homework Statement Solve: -D(x) \frac{d^2 T}{dx^2}=1 for x \in [0,1] D(x) =10-3 in [0,0.5] and D(x) = 1 in (0.5,1] with homogeneous dirichlet boundary conditions The Attempt at a Solution So I have two quadratic equations with x(0)=x(1)=0 and continuity at x=0.5 but I'm...

Homework Statement Solve the following problems using Laplace Transforms: y' - y = 2e^t, y_0 = 3 y'' + 4y' + 4y = e^{-2t}, y_0 = 0, y_0' = 4 y'' + y = sin(t), y_0 = 1, y_0' = 0 y'' + y = sin(t), y_0 = 1, y_0' = -\frac{1}{2} Homework Equations N/A The Attempt at...

the book gives u_{xx} - u_{tt} - au_{t} - bu = 0; 0<x<L, t>0 says if you multiply it by 2u_{t} you can get \left( 2u_{t}u_{x}\right)_{x} - \left( u^{2}_{x} + u^{2}_{t} + bu^{2}\right)_{t} -2au^{2}_{t} = 0 or \frac{\partial}{\partial x} \left( 2 \frac{\partial...

Homework Statement This is a discussion question from an online course I'm taking. 1. Find an example from engineering which involves a second order derivative. This 2nd order derivative should have some name. For example, the 2nd derivative of displacement with respect to time is called...

Homework Statement y'' + 9y = 2x2e3x + 5 Homework Equations N/A The Attempt at a Solution I think the complementary solution yc = c1cos(3x) + c2sin(3x). If not for that little +5 at the end of the right hand side, I'm pretty sure I could solve it. But I don't know how to include it in my...

First off I am NOT asking you to solve this for me. I'm just trying to understand the concept behind this problem. Let L be a linear transformation defined by L[p]=(x^2+2)p"+ (x-1)p' -4p I have not seen linear transformations in this format. Usually I see something like L(x)=x1b1+ x2b2...

Homework Statement Use the method of reduction of order to find a second solution of the given differential equation t2y'' - 4ty' + 6y, t>0; y1(t) = t2 The Attempt at a Solution Here's what I have so far: y = vt2 y' = 2tv + t2v' y'' = 2v + 4tv' + t2v'' so t2 (2v + 4tv'...

I have to start from a simple 2nd order ordinary deifferential equation as: y’’+2ξωny’+ω2y = F The solution should be of the form y = ∫F(Ω) G(t - Ω) dΩ (integral from 0-t) where G(t) = 1/ω * e^(-ξωnt)sin(ξt) for ξ<1 G(t) = e^(-ωnt) for...

Homework Statement I am attempting to solve the 2nd order ODE as follows using the generalized solution to the Bessel's equation Homework Equations original ODE: xd^{2}y/dx^{2}-3dy/dx+xy=0 The Attempt at a Solution My first thought is to bring out an x^-1 outside of the function so...

Suppose I have a 2nd order differential equation a_1y''(x)+a_2y'(x)+a_3y(x)+a_4=0 and two conditions y(0), y'(0). Then is there any theorem which gives us the condition under which the solution y(x) will be bounded? Note that x-range is entire real line. This is a general version of the...

Homework Statement I'd like to solve the following non-homogeneous second order differential equation and may I ask smart scholars out there to help me with this? y"(1-1.5(y')^2)=Cx^n, (^ denotes "to the power of") where C and n are constants, and the boundary conditions are: y=0...

Hi, it is well known that a second order ODe can be transformed into a system of two ODEs through the transformation u=y', v= y. Is the other way round possible? I mean, I have a system of 2 ODEs and want to transform it into a sucession on higher order problems that can be solved one after...

Hello everybody! Here are two ODE 2nd order I tried to solve, but I failed :( r''[t] - k/(r[t])^2 = 0 xy''[x] = ay[x] + b Could anyone of you please help me? Thanks in advance :)

Hello all, this is my first post and I'm having trouble with some homework. Here is the problem: Solve: U_x_y - yU_y = e^x I tried subbing V = U_y then I have V_x - yV = e^x I solve this as a linear equation with an integrating factor of e^{-\frac{1}{2}y^2} and get V =...

Hey everyone, Having some trouble here using the solver we were supplied and modifying it to fit our problem... I have a wire with a current flowing through it. I'm trying to find the temperature distribution wrt. position in the wire. BV's are: T(x=L/2) = 300K dT/dx (x=0) = 0 (Apparently...

Hello: Can anyone help me solve with the following nonlinear 2nd order differential equation? d^2 y/dx^2 (1+a(dy/dx)^2)=bx^c (a,b & c are constants.) Thank you. younginmoon

Homework Statement I had to solve the 2nd order d.e y'' + 4y' + 5y=0 Which I have done, then I need to find a solution for which y(0)=1 and y'(0)=0 The Attempt at a Solution My general soltuion for the d.e is y= e^(-2x) (c_1 *cos(x) + c_2*sin(x)) so for y(0)=1= e^0 (c_1 * 1 +...

Homework Statement find the general solution of y' = (y + y^2)/(x + x^2) The Attempt at a Solution I've tried a number of ways the first most obvious way I figured was to multiply the x+x^2 over so I did that but then when I expand I end up with a y' in both of the terms and I...

For the differential equation \frac{d^2y}{dx^2}+4 \frac{dy}{dx}=sinx One root of the auxiliary equation is '0' meaning the particular integral for the right hand side is x(Asinx+Bcosx). But is there any formal proof for making this claim that for 0 as one root is it is x(Asinx+Bcosx) or...

Homework Statement Solve the following system for \mathbf{r}(t): \frac{d^2\mathbf{r}}{dt^2}=-\frac{k}{m}\mathbf{r}.Homework Equations The Attempt at a Solution Now, I know how to solve for the magnitude of r (in fact, since it's the equation for the simple harmonic motion of a spring obeying...

Hi everybody, How do I solve this differential equation ??: y'' = a(Exp(-b*y)-1) ; where a, b are constants with the boundaries conditions : y'(x=0)=-K1 y'(x=L)=0 without the constant term I can do y''*y' = y' a Exp(-b y) then integrate it \ {1/2} (y')^2= {a/b}...

Find the general solution of the ordinary differential equation. y'' - 7y'+ 6y = 2e^(3t) + te^(t) First i found GS(H) by lettings y = e^(cx) and got GS(H) = Ae^(6t) + Be^(t) i then found PS(IH) y'' - 7y'+ 6y = 2e^(3t) by letting y = ae^(3t) and got PS(IH) = -(1/3)e^(3t) Now my...

Hello all, This is the first time I've stumbled across this site, but it appears to be extremely helpful. I am a meteorology grad student, and in my research, I have run across the following 2nd order non linear differential equation. It is of the form: y'' + a*y*y' + b*y=0 where a...

I thought this was rather odd, and wanted to just show it to see what you all thought of it. Well, also, if anyone knows what I should read to exactly understand what I did. 1: Let's define each answer of a polynomial such as (ax + b)(cx + d) as x1 = (-b/a), x2 = (-d/c). 2: The...

Does most of mathematics use 2nd order logic? If so would studying the foundations of mathematics involve mostly using 2nd order logic?

Homework Statement http://img178.imageshack.us/img178/6444/scan0001abq4.th.jpg Homework Equations The Attempt at a Solution this isn't a straight forward calculate the soltion to a 2nd ode so I am pretty stumped.

Homework Statement Prove that if y1 and y2 have maxima or minima at the same point in I, then they cannot be a fundamental set of solutions on that interval. Homework Equations Do I take the wronskian (determinant of y1, y1', y2, y2')? What would that tell me? The Attempt at a Solution

Homework Statement Show that id y = x(t) is a solution of the diff. eqn. y'' + p(t)y' + q(t)y = g(t), where g(t) is not always zero, then y = c*x(t), where c is any constant other than 1, is not a solution. Homework Equations Can someone help me get started? Also, since g(t) is not...

My question is in regards to converting a system of differential equations into a higher order differential equation. I am an undergrad taking diff eq and have just learned the wonders of Euler's method of solving 2nd order differential equations with constant coefficients. It is significantly...

Problem solving 2nd order ODE...not for the faint of heart! Hey folks, I'm having problems solving the following set of ODE's: 3H_a^2+H_b^2+6H_aH_b=k_1\rho eq.1 \dot{H_a}+3H_a^2+2H_aH_b=k_2\rho eq.2 \dot{H_b}+2H_b^2+3H_aH_b=k_3\rho eq.3 These are cosmological equations. Note...

Is there a numerical method for finding solutions to 2nd order non-homogeneous differential equations? Thanks.

2nd order diff Eq with t missing I am trying to find y as a function of t and y'' - y = 0 The two IV given are y(0) = 7, and y(1) = 5 .. Remark: the initial condition involves values at two points. Well since y = {y,y''} and the independent variable t does not appear, I went about it by...

1) Assume that p and q are continuous on some open interval I, and that y1 and y2 are solutions of y'' + p(t)y' + q(t)y = 0 on I. a) Prove that if {y1, y2} form a fundamental set of solutions on I, then they can't have a common inflection point in I, unless p and q are both 0 at this point...

Homework Statement Well I've got another one that totally sucks. y'' + 2y' + 5y = 4e^{-t}cos(2t) Homework Equations The Attempt at a Solution I tried Y(t) = Ae^{-t}cos(2t) + Be^{-t}sin(2t) but that unfortunately yielded 0 = 4e^{-t} cos(2t) So my question is how does one modify Y(t) in this...

Ok, so while I understand 2nd Order ODEs... I really don't understand MATLAB. I have 2 questions that I just can't get any code to work for: 1 Question: Consider the model of an undampened spring-mass system with a time-dependent spring constant k(t) given by: d2y/dt2 + k(t)y = 0...

[SOLVED] 2nd order differential - particular solution Homework Statement a) Find the general solution of the differential equation: \[2\frac{{d^2 x}}{{dt^2 }} + 5\frac{{dx}}{{dt}} + 2x = 2t + 9\] b) Find the particular solution of this differential equation for which: \[x =...

Homework Statement Hey, I am trying to approximate the solution to a second order ODE using the 4th order Runge-Kutta. I was told that in order to do this, I have to write the second order ODE and a pair of 1st order ODEs. Given that my differential equation is d^2v/dt^2 + adv/dt...

1. Homework Statement : This problem is in regard to a suspension system (mass, spring, dashpot) subjected to a 2 cm bump in the road. Given the mass and spring coefficient, we are to find: a) The minimum damping coefficient, c, to avoid oscillation. b) The expression for amplitude of...

If there is a differential equation to solve of the form a\frac{d^2y}{dx^2} +b\frac{dy}{dx} + cy = tan(x) you would put the LHS=0 and get the complementary function. But what would the the particular integral of tan(x) ?