2nd order Definition and 464 Threads

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Homework Statement Consider the following second order ODE $$ y'' + 2y' - y = e^{-x}, \quad y(0) = y'(0) = 1. $$ Convert this to a system of first order equations and use the pc33assisys MATLAB file to compute the solution for y(2). Homework Equations The Attempt at a Solution...

Homework Statement The problem states d^2y/dt^2 +15y= cost4t + 2sin t initial conditions y(0)=y'(0)=0 Homework Equations The Attempt at a Solution All I have is this r^2+15=0 making r(+-)=√15 and making yh= C1cos√15+C2√15 the next part includes solve for...

I have a problem which in involves a second order differential equations with imaginary roots and I can seem to know how to finish the problem. d^2y/dt^2 +15y =cos 4t+2 sin t this is what I got so far r^2+15=0 for the homogeneous part r=+-(√15) Yh=C1cos√15+C2sin√15 now is...

Hi PF, I would like to simulate N th order markov chain (not by means of hidden markov models, but ordinary markov chain) using Matlab. If n-th order is a heavy thing atleast 2nd or 3rd order will do. TIA

Homework Statement I'm having some trouble calculating the 2nd order energy shift in a problem. I am given the pertubation: \hat{H}'=\alpha \hat{p}, where $\alpha$ is a constant, and \hat{p} is given by: p=i\sqrt{\frac{\hbar m\omega }{2}}\left( {{a}_{+}}-{{a}_{-}} \right), where {a}_{+} and...

It's been a while since I've played with systems of ODEs, and I seem to have forgotten some of the tricks. As an example, I have two coupled nonlinear DE that I want to convert to a system of four 1st order nonlinear DE. But, the normal way of making variable substitutions is not working of...

Homework Statement I attached the problem because it's easier Homework Equations The Attempt at a Solution The main problem I have with this problem is trying to find the density as a function of radius. I have been thinking for hours but can't come up with anything. What I...

Homework Statement Here is the problem, verbatim. Observe that y=x is a particular solution of the equation 2x^2y''+xy'-y=0[\tex] and find the general solution. For what values of x is the solution valid? Homework Equations The Attempt at a Solution I know the answer is...

In my physics class we're talking about LC and LRC circuits, and the equations are analogous to those for SHM. However, I don't see how x=Acos(ωt+\varphi) satisfies m(d^2x/dt^2)+(k/m)x=0. I've never done differential equations and in the book it seemed like the author just guessed and checked...

Homework Statement The equation for the undamped motion with no rubber band: y" + k1y = -10 k1 = any number between 12 and 13 Find exact solutions using a couple different initial conditions And then plot this phase plane using some software The Attempt at a Solution So I know...

Homework Statement Consider the general linear homogeneous second order equation: P(x)y'' + Q(x)y' + R(x)y = 0 (1) We seek an integrating factor μ(x) such that, upon multiplying Eq. (1) by μ(x), we can write the resulting equation in the form [μ(x)P(x)y']' + μ(x)R(x)y = 0...

Homework Statement \frac{d^2 y}{dx^2}\cdot\frac{dy}{dx}=x(x+1), \hspace{10pt} y(0)=1, \hspace{5pt} y'(0)=2 Homework Equations None I can think of... The Attempt at a Solution The only thing I even thought to try was turn it into the form: \frac{d^2 y}{dx^2}{dy}=x(x+1){dx}...

How can I extract time data from a system 2nd order ODEs in Mathematica?

I am intending to use Runge Kutta 4th order to numerically solve a system of coupled equations: \frac{d^{2}x}{dt^{2}} = K1 * x * cos(t) + ( (K2 * \frac{dy}{dt}) - \frac{dz}{dt} ) \frac{d^{2}y}{dt^{2}}= -K1 * y * cos(t) + ( (K2 * \frac{dz}{dt}) - \frac{dx}{dt} )...

Homework Statement Find general solution to: xy''+2y'+4xy=0 Homework Equations Frobenius Method or Bessel's Equation The Attempt at a Solution I know how to get the roots for this problem (which are r1 = 0 & r2 = -1). But not I don't know what to do with these roots. I know that...

I am getting this error in Mathematica from the code below: Computed derivatives do not have dimensionality consistent with the initial conditions ClearAll["Global`*"] \[Mu] = 398600; s = NDSolve[{x1'[t] == x2[t], y1'[t] == y2[t], z1'[t] == z2[t], x2'[t] == -\[Mu]*x1[t]/(x1[t]^2 +...

Can this second order be changed into a system of first order: $$ x''(t) = -\frac{\mu}{(\sqrt{x^2+y^2+z^2})^3}x $$

1. Homework Statement B, K, M 2. Homework Equations 1. xs(t) -----spring ----mass-----damper-----fixed, derive DE for x of mass given :2. F - > M -----spring-------damper ---- fixed in series, derive the DE for velocity of spring 3. The Attempt at a Solution 1. ma =...

Homework Statement B, K, M Homework Equations 1. xs(t) -----spring ----mass-----damper-----fixed, derive DE for x of mass given :2. F - > M -----spring-------damper ---- fixed in series, derive the DE for velocity of spring The Attempt at a Solution 1. ma = -k(x-xs) -...

Homework Statement 1.)I want to write a function in MATLAB that contains the 2nd order function: 20*d^{2}x;(dt^{2})+5*dx/dt + 20*x=0 (dampened spring) -The function should have 2 inputs (time,[initial values]) initial values should be a vector of 2 values -The function should...

I'm trying to work out the Transfer function for the 2nd order RC circuit in the attachment below: I can't seem to get the right answer :( circuit: My answer: Please see attachment for my attempt and the relevant information:

Hi, When solving a 2nd order Linear DE with constant coefficients (ay''+by'+cy=0) we are told to look for solutions of the form y=e^{rt} and then the solution (if we have 2 distinct roots of the characteristic) is given by y(t)=c_1 e^{r_1 t}+c_2 e^{r_2 t} This is clearly a solution, but...

A second order system has the following standart form; http://controls-design.com/mathtex/mathtex.cgi?H%28s%29%3DK%5Cfrac%7B%5Comega_n%5E2%7D%7Bs%5E2%2B2%5Czeta%5Comega_n%20s%2B%5Comega_n%5E2%7D%20%5Cmbox%7B%20for%20%7D%200%20%5Cle%20%5Czeta%20%5Cle%201 However, sometimes the system I...

I have to derive equations of motion from Lagrangian and stumbled upon the following system of equations (constants are simplified, that information is unneeded) \begin{cases} \ddot{x}-A\dot{y}+Bx=0 \\ \ddot{y}+A\dot{x}+Dy=0 \end{cases} This is an extension of a simpler problem where B=D...

Homework Statement I have the following difference equation; y[n] -1.7y[n-1] -0.72y[n-2]=x[n] with aux conditions; y[-1]=1, y[-2]=-2 input; x[n] = (0.7)^{n}u[n] I used the recursive method to get 5 consecutive values of the impulse response of the system and also 5 consecutive values of...

Homework Statement I was given a DE of the form: \Phi^{''}+(6/\eta)\Phi^{'}=0 where the next step was given as \Phi^{'} \propto \eta^{-6} where the answer came out to be \Phi \propto \eta^{-5} + constant The Attempt at a Solution My attempt was to set \Phi^{'}=x where I would then get...

Homework Statement I have to determine the 2nd,3rd and 4th derivative at 0. So ψ''(0) The equation is y'' + sin(x)y' + cos(x)y = 0 A know solution is y = ψ(x). The intial conditions are y(0) = 0 , y'(0) = 1 Homework Equations The Attempt at a Solution I know this is a...

Homework Statement Show that y(t) = (1/w) ∫[0,t] f(s)*sin(w(t-s)) ds is a particular solution to y'' +w2 y = f(t)where w is a constant. The Attempt at a Solution After wasting several pages of paper I have made virtually no progress. Obviously, substitution suggests you plug in y(t)...

Hi, I'm fitting a distribution to the starting times of the first car journey in the day. I have a sample of 3,000 journey starting times. I am assuming that this sample represents the population well. I'm fitting a non parametric distribution. But my question is, should I fit a 1st...

The question is to solve the equation y'' + ω^2y = cos(ωt) I know you'll find the complementary and particular functions and add them together. Now I found the complementary function easily. r= +/- ωi and then plug into the general equation for complex numbers. The problem I have is...

Homework Statement 4y''+4y'+y = cos(2t), y(0)=0, y'(0)=0 Homework Equations y(t)=yh+yp The Attempt at a Solution characteristic roots are repeated, m=-1/2, so y_h = A_1 e^{\frac{-t}{2}}+A_2 te^{\frac{-t}{2}} undetermined coefficients: yp = Acos(2t)+Bsin(2t) plugging into original...

Homework Statement Find the general solution to d2y/dx2 +4y=cos(2x) Homework Equations The Attempt at a Solution I have woked out what I think is the Complementary function C1sin(2x)+C2cos(2x) the reason it is cos and sin is because the roots are 2i and therefore the exponential...

Homework Statement Derive the Derive the two variable second order Taylor series approximation, below, to f(x,y) = x^3 + y^3 – 7xy centred at (a,b) = (6,‐4) f(x,y) ≈ Q(x,y) = f(a,b) + \frac{∂f}{∂x}| (x-a) + \frac{∂f}{∂x}|(y-b) + \frac{1}{2!}[\frac{∂^2f}{∂x^2}| (x-a)^2 + 2\frac{∂^2f}{∂x∂y}\...

Homework Statement 64y''+144y'=0 y1(0)=1 y'1(0)=0 and y2(0)=0 and y'2(0)=1 Homework Equations y1=c1*e^(r1*t) + c2*e^(r2*t)The Attempt at a Solution I start by finding the characteristic equation: 64r^2+144r=0 r1=-9/4 and r2=0 y1=c1e(r1*t) + c2e(r2*t) so I get y1=c1e^(-9/4 *t) + c2e^(0*t)...

Hi, How can one use back Euler method for 2nd order d.e? Is it possible this method to be expanded for a system of 4 odes? Thanks

I have a problem with differential equations - 2nd order - reduction of order my problem is as follows: (x − 1)y" − xy' + y = 0 , x > 1 ; y_1(x) = e^x solving this type of diff. eq. says to use y=y_1(x)V(x) which gives me y=Ve^x differentiating y gives me y'=V'e^x & y''=V''e^x...

Homework Statement y"-2y'+5=0, y(∏/2)=0, y'(∏/2)=2 find general solution of this diff eq Homework Equations The Attempt at a Solution i have followed all of the steps for this, rather easy 2nd order diff eq, but i my solution differs from the books solution. steps...

A first order DE models the rate of change, e.g. when decay is proportional to time we have the DE: dM/dt = -K.M; this is describing that rate of change mathematically. Am I correct in saying that a 2nd order DE describes the rate of rate of change? Also, can anyone explain any application of...

Hi, I am completely stuck on this problem that has been given to us. I must solve a set of 2nd order differential equations using Euler's method. It is for a geosychronous orbit of a satellite, meaning the orbit is circular and the velocity vector is perpendicular to the radius vector...

Hi all Quick one, if one had an equation y' = x on could simply separate the variables and integrate. Now it the equation y'' = x you would use separation of variables what drives this? Also y'' =0. Is the same as. y''dx =0 dx Why is this legal?Thanks in advance

Homework Statement Find a solution (Z2) of: z'' + 2z - 6(tanh(t))2z = 0 that is linearly independent of Z1 = sech2Homework Equations The Attempt at a Solution reduction of order gives you v''(t)(Z1(t))+v'(t)(2 * Z1'(t)) + v(t)(Z1''(t)+p(t)Z1'(t)) = 0 however the third term on the LHS can be...

To my knowledge I assume: Newton's second law of motion : F = ma = mx'' Hooke's Law F = ks where s is the distance displaced by the mass. When a mass is attached to the spring, the new spring force is: F = k(s+x) While the downward force is still: mg If the two forces...

"separation of variables", but for 2nd order Ok, I know how to separate variables in solving an ODE. I am unable to understand a solution I have for a problem which was the result of reduction of order- we end up with u''*sinx-2u'*cosx=0 so turn this into u''/u'=-2cosx/sinx At this point I...

Homework Statement Find the general solution to the following differential equation: \frac{d^2 y}{dt^2} - 2 \frac{dy}{dt} + 2y =e^t The correct answer must be: y(t) = C_1 e^t \cos t + C_2 e^2 \sin t +e^t The Attempt at a Solution I haven't been able to get the correct answer so far. The...

I got trouble in dealing with this kind of system. For example, Ay``+By`+Cy=0 where y=transpose(y1 y2) A=(1 0 0 1) B=(0 1 1 0) C=(1 1 1 1) May someone give me a book name?:smile:

2nd Order Homogenous ODE (Two solutions??) Alright. I understand that if we have a differential equation of the form A\cdot\frac{d^{2}y}{dt}+B\cdot\frac{dy}{dt}+C\cdot y = 0 and it has the solution y1(t), and y2 is also a solution. Then any combination of the two yH=C1y1(t)+C2y2(t)...

I got some questions about this topic... y'' + p(z)y' + q(z)y=0 where y (and its derivatives) is a function of z, z ∈ ℂ. 1) My books says this: In points where both p(z) and q(z) are analytic, y(z) is also analytic. But in points where p(z) or q(z) (or both) aren't analytic, y(z) may not...

Homework Statement Find the voltage across the resistor. Homework Equations V = L*di/dt I = C*dv/dt The Attempt at a Solution I'm not too worried about the differential equation part but I need some help setting up the circuit for me to start the process. Since the current through the...

Hi I am trying to integrate Newtons equations for my system a = \frac{F}{m} = \frac{d^2x}{dt^2} This is only for the first coordinate of the particle. I wish to do it for y and z as well, but let us just work with x for now to make it simple. The force in the x-direction depends on...