Second order Definition and 570 Threads

Homework Statement Hi I need to solve the following: \frac{d^{2} x}{dt} + 2 b \frac{dx}{dt} + (b^2 - \frac{db}{dt}) x = 0[/tex] 2. The attempt at a solution Isn't this equivalent to??:: [itex]x^{''} + 2bx^{'}+ (b^2 - b^{'})x = 0 \iff x^2 + 2x +1 = 0 If I let b = 1. which...

hello every body .I have some problem : i don't know slove the equation x"=k/m*x (1) i don't understand result of (1) is x=Asinkt+Bcoskt

Hi everyone. I am really confused at the moment learning about Second Order homogeneous linear differential equations. I lay out the background of what I would like to understand. So I understand the actual maths that goes into the diff's, but I do not understand why it should be so, given the...

ive been doing Xdot and Ydot questions using the formula lamda2-(a+d)lamda +ad-bc=0 where Xdot=ax+bc and ydot=cx+dy no problems so far until this question where i have the second order equation xdot dot+x-1/4x3=0 so i set Xdot dot =Ydot and therefore Xdot =y as usual but this gives me...

Homework Statement A 32 pound weight stretches 2 feet. Determine the amplitude and period of motion if the weight is released 1 foot above the equilibrium position with an initial velocity of 2 ft/s upward. How many complete vibrations will the weight have completed at the end of 4 pi seconds...

Homework Statement I have no idea about how to solve the second order differential equation. Please someone help me solve this. Or provie me some articles for beginnrs. I have only basic knowldge of calculus. While solving a question at physics, I got this...

Hey guys. I need to know how to draw a Phase Bode plot of a Second order system. I understand and can draw the Gain(Magnitude) Bode plot, but I can't seem to get the grip of the Phase one. As far as I know there is an asymptote at 0^{o} at low frequencies and an asymptote at 180^{o} at...

I just finished a final in my differential equations class. One of the problems had me solve a second order homogeneous differential equation using series. I boiled it down to this recursion relation: a_{n+2}=\frac{(n+3)a_{n}}{2(n+2)(n+1)} I found that the even coefficients work out...

Hey; not much of a homework question, but something i was wanting to find out. Im still a first year undergraduate and just started on differential equations. We have just finished going over homogeneous 2nd order ODE's of the form: ay'' + by' + cy = 0 My texbook briefly outlines the...

hey I am having a little trouble with this topic. Here are the questions I was set. a) Find the general solution of d^2y/dt^2 - 2(dy/dt) + y = 0. Verify your answer. b) Solve the initial value problem y'' + 4y' + 5y = 0; y(0)= -3, y'(0) = 0 c) Find a DE that has the given functions as...

Hello. I am an engineering student and am having trouble trying to figure out how to solve this system of second order, nonhomogeneous equations. I know how to solve a single second order, nonhomo. equation and how to solve a system of first orders, but not this one. Any help would be greatly...

Homework Statement A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an externam...

Homework Statement a) Show that phi(t) = e^2t is a solution of y' - 2y = 0 and that C*phi(t) is also a solution for any constant C b) Show that phi(t) = 1/t is a solution of y' + y^2 = 0 for t>0 but that y = c*phi(t) is not a solution unless c = 0 or c = 1 Homework Equations What do...

y'' - 8y' + 16 = 0 ; y(0) = 4 ; y'(0) = 9 this should be not too bad but I am stuck in the same place. m^2 - 8m + 16 m1 = m2 = 4 y = C1e^(mx) + C2(e^(mx)) sub in y(0) = 4 4 = C1 + C2 C1 = 4-C2 y' = mC1e^(mx) + mC2e^(mx) sub in y'(0) = 9 9 = mC1 + mC2 C1 = 4 - C2...

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...

It's been a while since I've had DE, and it seems I have forgotten something basic, yet crucial. In solving the Time-Independent Schrodinger Wave Equation in one dimension, I have the following: \left( -\frac{\hbar}{2m} \frac{\partial^2}{\partial x^2}+V\right) \Psi(x)=E\Psi(X)...

Homework Statement I have two questions: 1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1) 2)I have two second order ODES X''=... and Z''=... to solve this, we make the...

[SOLVED] Nonhomogenous Second Order DE Homework Statement y'' - 2y' - 3y = -3te^{-t} SolveHomework Equations The Attempt at a Solution Well first I tried Y(t) = Ate^{-t} then Y(t) = At^2e^{-t} then Y(t) = At^3e^{-t} and Y(t) = At^3e^{-t} + Bt^2e^{-t} but I can't seem to get the correct...

Hi every one ! I am a final year Engineering student of IIT Madras, India. I am doing a project(finite element analysis of a structure) which requires the solution of a system of second order differential equations. equation looks like below: [M][U"]+K[U]=[F(t)] M : Mass Matrix of size...

Second order diff.eq. help?? well i am trying to find a solution to this diff. eq, but i get stuck somewhere. \ 4x^{2}y''+y=0 I first took this substitution y'=p, y"=p' so the diff. eq becomes of this form \ 4x^{2}p'+p=0 i think this can be done with the separable of variables...

Homework Statement solve y"+y=xsin(x) , initial conditions y(0)=0, y'(0)=1 Homework Equations The Attempt at a Solution I know that when right hand side equals something like sin(x), then the particular integral is xc1sin(x)+xc2cos(x). I am unsure what the particular integral...

Homework Statement Solve the reducible 2ODE. Assume x, y and/or y' positive where helpful. y^3 * y'' = 1 The Attempt at a Solution Well, I tried what I normally would do for x being missing. p = (dy/dx); y'' = p'p = (dp/dy)(dy/dx) So y^3 p'p = 1 p(dp/dy) = y^(-3)...

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...

Homework Statement Consider the second order differential equation y'' - 4y' + 4y = f(x) Find a particular solution if f(x) = 25cos(x) Homework Equations I believe for this type of question I should let y = Asin(x) + B cos(x) Hence y' = Acos(x) - Bsin(x) and y'' = -Asin(x) -...

Quadratic Polynomial can't satisfy second order linear differential equation with constant coefficients... WHY? and if possible, how would I show this? Does it have to do with independence?

I am sure most of you are familiar with the equation: m(x)''+c(x)'+k(x) = 0. Then, we create an auxillary equation that looks like this: mr^2+cr+k = 0. And, then we find the roots of this auxillary equation, calling them r1 and r2. And, if the roots are r1,r2>0 we consider the system to be...

Solve by direct substitution taht the function \phi(t) = Asin(wt) + Bcos(wt) is a solution of the second order differential equation \ddot{\phi} = -w^{2}\phi. ( Since this solution involves two arbitrary constants - the coeffecients of the sine and consine functions - it is in fact the general...

I need to solve the equation \frac{d^{2}}{dx^{2}}\Psi + \frac{2}{x}\frac{d}{dx}\Psi = \lambda\Psi Can anyone help me get a start on this problem? I've been guessing at a few solutions with no results... I'm not asking anyone to solve the problem... just a few hints on starting... maybe...

Homework Statement Have to use the product rule twice. \frac{d}{dx}=x^4e^xsin(x)[/itex] I got about as far as the first use of the product rule then stalled when I had to use it again. got this:- (1+x^2)sin(x)+(x^4e^x)sin(x) but not this:- (4x^3e^x+x^4e^x)sin(x)+x^4e^xcos(x) Problem is...

Hello everyone The following two differential equations appear on page 93 of George Simmons' book on Differential Equations. While I have been able to solve them, I have some questions. [Not HW] I. (x^2-1)y'' - 2xy' + 2y = (x^2-1)^2 II. (x^2 + x)y'' + (2-x^2)y' - (2+x)y = x(x+1)^2 How I...

Homework Statement In the circuit below, determine v_o(t) for t > 0. Let V_{IN}\,=\,u(t)\,V, R_!\,=\,R_2\,=\,10\,k\Omega, C_1\,=\,C_2\,=\,100\,\muF. http://img249.imageshack.us/img249/3840/problem867cg5.jpg Homework Equations i_c\,=\,C\,\frac{dv_c}{dt} The Attempt at a...

Homework Statement Obtain i_1 and i_2 for t > 0 in the circuit below. http://img258.imageshack.us/img258/7765/problem60as1.jpg Homework Equations V_L\,=\,\frac{di_L}{dt} The Attempt at a Solution To get initial conditions, I made a second circuit diagram for t < 0...

Homework Statement http://img396.imageshack.us/img396/2781/chapter8problem55oy6.jpg For the circuit above, find v(t) for t\,>\,0. Assume that v\left(0^+\right)\,=\,4\,V and i\left(0^+\right)\,=\,2\,A. Homework Equations i_c\,=\,C\,\frac{d\,v_c}{dt} The Attempt at a Solution I made a new...

Homework Statement This is the result of a problem from my Quantum class, but I figure it would be best to ask in here as my question is purely a question of how to solve a certain differential equation. the equation is of the form 0=Y''-i*a*Y' + b*Y where Y is a function of t So the...

In general how do we deal with linear second order differential equations with variable coeffecients?

Here's the problem: x^2y''-3xy'-12y=0 with initial conditions y(1)=0 and y'(1)=7 I'm supposed to solve for y in the form y=c1y1+c2y2 y1 = x^6 by inspection Now to solve for y2 y2=y1v v can be solved for by the equation y1v''+(2y1'+py1)v'=0 where p is the function in front...

Crap, nevermind, I left b^2 out of the quadratic formula, thanks anyways. Here's the question: Find y as a function of t from the diff eq: y''+6y'+25y=0 with the initial conditions y(0)=8 and y'(0)=8 I used the form r^2+6r+25=0 to solve for r and through the quadratic equation got r =...

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...

d2y/dx2+k*dy/dx = du/dx+u anyone got a hint how to use ODE to sovle this inhomogenous equation? Thanks a lot

Second Order Equations! Can Anybody help me?? Greatly appreciated! Homework Statement Interpret x(t) as the position of a mass on a spring at time t where x(t) satisfies x'' + 4x' + 3x = 0. Suppose the mass is pulled out, stretching the spring one unit from its equilibrium position, and...

Homework Statement Homework Equations HalfLife = 1 / k*[A]i where k is the rate constant and [A]i is the initial concentration of a reactant A. The Attempt at a Solution I don't have enough information to attempt this problem. I don't know what to do with the partial pressure...

I need help solving this equation y''+y'+y= sinx I know it looks simple but It seems to be getting sticky! I have been trying to solve it using variation of perimeters,maybe there is a quicker way? If anyone can help please...:bugeye:

I need some help on finding the general solution. I can find the complimentary solution, I'm having trouble finding the particular solution. Can anyone give me any tips. y"+9y=t^2e^(3t)+6 y"-2y'-3y=-3te^-t y"+2y'=3+4sin(2t)

I am having real trouble with this second order differential The substitution is given and i just can't seem to use it What am i missing here? x \frac{d^2 y} {dx^2} -2 \frac{dy} {dx} + x = 0, \frac{dy} {dx} = v All help welcome

Hi All, I have a differntial equation that I came up with on a little engineering problem posted here https://www.physicsforums.com/showthread.php?t=129247 that I can't solve. It is d^2R/dt^2=W^2*R where R is radial position and W is angular velocity and t is time. I think it is an autonomous...

I was wondering what the best method is to solve two second order differential equations that are coupled. I need to solve it by hand and write my own code so I cannot use built in functions in matlab, etc. At time (0), displacement and velocity are 0 with an initial acceleration which is...

A simple question i think although i can't find in any books What do u when u are solving a second order linear hoemoeneous differential equation with frobenius and there is no shift. (X^2)(y^{''}) (-6y)=0 it should be normal minus -6y I only know what to do if there...

Are there any analytical solutions to: ay''+bx^2y+cxy+dy=0 where a,b,c,d are constants and y(x) If so how would you go about it? Is there a website that teaches you how to solve these?

I'm using the method of undetermined coefficients here, but I'm either not making the correct ansatz or I'm just confused on the method. The problem is 2y'' + 3y' + y = t^2. I gussed Y = At^2. Is this correct? It doesn't solve the differential equation, which is the only check I know...

I just came across this one, was going really well until i came across this one. (d^2y/dx^2) + (dy/dx) = e^(-x) m^2 + m = 0 m = -1 and m = 0 Now i get the particular integral Try y = ke^(-x) (dy/dx) = -ke^(-k) (d^2y/dx^2) = ke^(-x) ke^(-x) - ke^(-x) = e^(-x) I get stuck here...