2nd order Definition and 494 Threads

$\tiny{17.2.02}$ \nmh{1000} $\textrm{Solve the equation by the method of undetermined coefficients.}\\$ \begin{align*}\displaystyle y''-4y'&=\sin{x}\\ y_p&=A\sin{x}\\ \end{align*} $\textit{ answer}$ \begin{align*}\displaystyle y{\left (x \right )}& = C_{1} + C_{2} e^{4 x} - \frac{1}{17}...

Imagine I have a complicated second-order differential equation that I strongly suspect can be derived from a Hamiltonian (with additional momentum dependence beyond p2/2m, so the momentum is not simply mv, but I don't know what it is). Are there any ways to test whether or not the given...

Can someone check my work here? Both ##f=f(x)## and ##y=y(x)##. $$f'y'+\frac{fy''}{1+y'^2}=0\implies\\ \frac{y''}{y'(1+y'^2)}=-\frac{f'}{f}\\ \frac{y''}{y'(1+y'^2)}=-\ln(f)$$ Now let ##v=y'##, which implies $$...

I have a differential equation that is essentially this: θ''(t)=c*sin[θ(t)] . I've been stymied trying to find a solution, and even when I tried using Maple, I got a nasty integral of a Jacobian amplitude. I'm tempted to use a small angle approximation, but the angle is 0≤θ≤π/2. I know this...

Homework Statement Consider the initial value problem x" + x′ t+ 3x = t; x(0) = 1, x′(0) = 2 Convert this problem to a system of two first order equations and determine approximate values of the solution at t=0.5 and t=1.0 using the 4th Order Runge-Kutta Method with h=0.1. Homework Equations...

Homework Statement How exactly they combined equation1 and equation2 and got that system? I don't get that part. Homework Equations A*(dy/dt)= -k*y eq1 A*(dz/dt)=ky-kz eq2 The Attempt at a Solution I tried substituting the 1st ky in the 2nd equation and then differentiating but I don't...

Homework Statement Homework Equations N/A The Attempt at a Solution I understand how they got the answer and the calculations they did but I have 3 questions about this screenshot. 1) Why the box in red is the transfer function? Is there a way to tell this from the Y(s) = ... expression? 2)...

I have ##\frac{d^2x(t)}{dt^2} + B(x(t))^3 = 0## for a system where I know the initial conditions and where B is a constant that's constructed from the properties of the system. I would like to find ##x(t)##. I've modeled the system in Python and produced some graphs. I know that ##x(t)## is...

xy'' + 2xy' - y = 0 Honestly no clue where to start, Wolfram Alpha gives a rather complex answer lol (http://www.wolframalpha.com/input/?i=xy%27%27%2B2xy%27-y%3D0)

As an exercise, I am trying to solve the 2nd-order wave equation: $$ \frac {\partial ^2 E}{\partial t^2} = c^2 \frac {\partial ^2 E}{\partial z^2} $$ Over a domain of (in SI units): ## z = [0,L=5]##m, ##t = [0,t_{max} = 5]##s, ##c = 1## m/s and boundary/initial conditions: ## E(z[0]=0,t) =...

Homework Statement Find the general solution for the DE: t2y''-2y=0 Homework Equations These were given for other parts of the problem so I'm not sure if they're relevant. y1(t)=t2, y2(t)=t-1, y(1)=-2, y'(1)=-7 The Attempt at a Solution The t2 at the front was really stumping me and I'm not...

Homework Statement Uxx - SU = A ; 0<x<1 Boundary conditions : Ux(0) = 0 U(1) = 0 The Attempt at a Solution I tried to set a new variable W = u + A, I can get rid of the A in the main equation and U(1) becomes = 1. If I set U= C*esqrt(S)x into the equation, its a trivial solution because of...

Is it possible to make a 2nd order CR LPF or HPF where the cut off frequencies for each pole are equal? Here is a calculator for this system which includes the transfer function.http://sim.okawa-denshi.jp/en/CRCRkeisan.htm I figured that I need to try to solve the denominator of the transfer...

Good morning everyone. First let me thank you for your help in advance! I have to solve this 2nd order non-linear ODE, and I'm stuck at the beginning. We have to find the equilibrium points, linearize the system, draw the phase portraits and classify the eq points, and solve it numerically. I...

Hi, This question on PD control is from a practice quiz. 1. Homework Statement If you can't see it- the question asks to find values for Kp and Kd such that the system achieves 5% OS and has a settling time Ts of 3s. Cs = 3 Cd = 2 m = 5Homework Equations ω_n^2/(s^2 + 2ζw_n + ω_n^2) - 2nd...

Given a linear homogeneous 2nd order ODE of the form $$y''(x)+p(x)y'(x)+q(x)=0$$ the general solution is of the form $$y(x)=c_{1}y_{1}(x)+c_{2}y_{1}(x)$$ where ##c_{1},c_{2}## are arbitrary constants and ##y_{1}(x), y_{2}(x)## are linearly independent basis solutions. How does one prove that...

Good day all I am struggling with this one. m (d^2 h)/(dt^2 )+k dh/dt=-mg use v=dh/dt in place to turn 2nd order into 1st order so from this i have got (d^2 h)/(dt^2 )= -g-(v/m) Is this a first order equation? If so can somebody point me to solve the equation when m=80, k=8.7, v(0)=0ms-1...

MX''=Fn(cosΦ−usinΦ) MZ''=Fn(sinΦ+ucosΦ)−Mg MΦ''=Fn(Bxx+uBz) I tried using Runge-Kutta methods to approximate motion equations in MATLAB but it turn out wrong. I also tired finding and researching forums and web for solution but to no avail. Fn,M,θ,u is constant fn/M = 0.866 it seems that i...

Homework Statement Hi There! MX''=Fn(sin θ - uCos θ ) MZ''=Fn(cos θ + uSin θ ) - Mg Fn,M,θ,u is constant fn/M = 0.866 M = 6000 θ = 30 u = 0.5774 i split my motion equation into 2 individual 1st ode, X' = Vx Z' = Vz Vx'=[fn*(sin θ - uCos θ )]/M Vz'={[fn(cos θ + uSin θ )]/M} - g...

I understand how to use the reactance equations (for capacitor, xc=1/(2PiFC), & for inductor xL=2PiFL when the filter circuit is of first order to get the component values I need, but I don't understand how the math works when the circuit is of second order. The man at the electronics store told...

{ i feel that this is Not a smart question and that it is about the basics of something , but i tried to find the that "something" to know about it myself but i couldn't , as i couldn't name the issue , so i couldn't know what to search about that is why I'm asking here in a forum , so please...

Hello. I forgot the reason why 2nd order differential equation has two independent solutions. (Here, source term is zero) Why 3 or 4 independent solutions are not possible? Please give me clear answer.

Homework Statement Find the general solution f(t) of the differential equation: f''(t) − f'(t) − 12f(t) = 36π . How many free parameters enter the solution, and why? Homework Equations f = fH + fP where fH is the homogeneous solution and fP is the particular solution. The Attempt at a...

if we assume the condition immediately after switch is closed (t=0+), *Capacitor voltage cannot jump. *Inductor current cannot jump. dv(0+)/dt=i_c(0+)/c di(0+)/dt=v_l(0+)/L which means we can find the initial condition of the post-zero system algebraically. However, it contradcits to the...

It's been too long guys. I've given this ODE lots of thought and still no cigar. Homework Statement We are given the following ODE: $$ (x-a)y''-xy'+a^2y = a(x-1)^2e^x $$ and knowing that y=e^x is a solution to the homogenous equation, find the possible values of a. Next part: Using the...

Homework Statement Hi,I am learning to solve 2nd-order differential eq. Suppose I have a equation dy/dx - 3x = 0...(1) Then dy/dx = 3x -----> x = 3(x^2)/2 Now if I have a 2nd order ODE such that: d^2y/dx^2 = 3....(2) Then it could be solved by integrating both sides wrt x twice,which yields y...

Homework Statement Y''-((Y')^2)+(C1*exp(Y))=C2 C1 and C2 are constants. exp = e Homework Equations No clue how to start this The Attempt at a Solution Y'=A=dY/dt Y=At+C3 (not sure) A'-(A^2)+C1exp(At+C3)-C2=0 A'-(A^2)+C1exp(C3)exp(At)=0 let C=C1*exp(C3) A'-(A^2)+Cexp(At)=0

I'm writing a paper about the projectile motion with the consideration og air resistance - I have obtained two formulas: ax = k*(vx2+vy2)0.5 * vx ay = k*(vx2+vy2)0.5 * vy - g (K and g are constants; K = -0,02, g =9,82) I cand write these two as 2 different differential equations: v'x(t) =...

Homework Statement Demonstrate that matrix ##T## represents a 2nd order tensor ##T = \pmatrix{ x_2^2 && -x_1x_2 \\ -x_1x_2 && x_1^2}## Homework Equations To show that something is a tensor, it must transform by ##T_{ij}' = L_{il}L_{jm}T_{lm}##. I cannot find a neat general form for ##T_{ij}##...

1. Problem statement: Assume that u is a vector and A is a 2nd-order tensor. Derive a transformation rule for a 3rd order tensor Zijk such that the relation ui = ZijkAjk remains valid after a coordinate rotation.Homework Equations : [/B] Transformation rule for 3rd order tensors: Z'ijk =...

I'm supposed to use undetermined coefficients to find a general solution to: y" + 4y' +3y =4^(-t) I can't find an example online where f(t) is equal to an exponential function that does not have e as the base, so I have no idea how to solve it. So far, I found the general solution to the...

I want to convert this linear second order general form PDE to two equations: ##ϕ_{xx}+bϕ_{xy}+cϕ_{yy}+dϕ_x+eϕ_y+fϕ=g(x,y)## Converted equations: ##a_1 u_x+b_1 u_y+c_1 v_x+d_1 v_y=f_1## ##a_2 u_x+b_2 u_y+c_2 v_x+d_2 v_y=f_2## I want to find parametric values of ##a_1 ...f_2## How can I do...

Homework Statement write the 2nd order taylor series for the log barrier function $$-\sum_{i=1}^{m}(b_{i}-a_{i}^{T}x)$$ Homework Equations See Above The Attempt at a Solution Here is my attempt at a solution $$\nabla...

In a book of math, I found a kind very very crazy of equation, an "variational equation of second order" So, my question is: exist solution for an general equation like this: A \frac{d^2}{dx^2} \frac{\partial F}{\partial y^{(2)}} + B \frac{d^1}{dx^1} \frac{\partial F}{\partial y^{(1)}} + C...

Given standard ODE $ y'' + P(x)y' + Q(x)y=0 $, use wronskian to show it cannot have 3 independent sltns. Assume a 3rd solution and show W vanishes for all x. so 1st row of W = {$ {y}_{1}, {y}_{2},{y}_{3} $}, 2nd row is 1st derivatives, 3rd row is 2nd derivatives. I can find the determinate...

Homework Statement Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients. For: y'' + 2y' + 10y = x^2e^{-x}\cos{3x} There's a modification performed and I'm not 100% confident as to why. Homework EquationsThe Attempt at a Solution The...

Homework Statement Regarding the case where the auxillary (characteristic) equation has complex roots, we solve the quadratic in the usual way using i to get the general solution y(x) = e^{\alpha x}\left(C_1 \cos{\beta x} + i C_2 \sin{\beta x}\right) And the textbook shows y(x) = e^{\alpha...

Homework Statement y'' + y' + xy = 0 Just want to make sure I understand this completely, I had a bit of trouble towards the end, and thought the -29/600 was a little weird of a fraction to be right. I wasn't given a correct answer to base mine off, so I'm not sure if I'm doing this all...

I've been searching for exact solution of d2y/dx2 = C/y, where C is some constant, such equation take place when deriving equation of motion in gravitationnal field, I'm more interested in how to solve it, yet I only managed to express it as power series using taylor's theorem at x = 0, just...

Homework Statement Solve the initial value problem Homework Equations Quadratic Formula The Attempt at a Solution My problem is that I don't understand how to solve the constants now, I understand, 2 equations, 2 unknowns, but when I plug the y(0) = 0 into the YsubH equation...

2nd order ODE has a form y''+p(x)y'+q(x)y=f(x)and if we assume f(x)=/=0 for every x, then y''+p(x)y'+q(x)y=/=0 so in this case we can't specify general solution of 2nd order ode?

Homework Statement $$ay''-(2x+1)y'+2y=0$$ subject to ##y(0)=1## and ##y(1)=0## where ##a## is a non-zero constant. Homework Equations Not too sure The Attempt at a Solution I know an analytic solution exists since I solved with mathematica. My thoughts were to try a series expansion, but...

Homework Statement Convert the following second-order differential equation into a system of first-order equations and solve y(1) and y'(1) with 4th-order Runge-kutta for h=0.5. ##y''(t)+sin(y(t))=0,\ y(0)=1,\ y'(0)=0## Homework Equations The Runge-kutta method might be applicable, but I know...

Homework Statement Solve d2θ/dη2 + 2η(dθ/dη) = 0, to obtain θ as a function of η, where θ=(T-T0)/(Ts-T0) EDIT: I should add that this is a multi-part problem, and η is given as η=Cxtm. We had to use that to derive the equation in question above.. So I don't know if this is supposed to be...

Hello, I am trying to understand how to get the residue as given by wolfram : http://www.wolframalpha.com/input/?i=residue+of+e^{Sqrt[x^2+%2B+1]}%2F%28x^2+%2B+1%29^2 The issue I am facing is - since it is a second order pole, when I try to different e^{\sqrt{x^+1}} I get a \sqrt{x^+1}...

Homework Statement Okay, here's the deal:I have been given a second order nonlinear differential equation, and I have also been given the general solution with constants A and B. I am supposed to find the constants A and B. The solution represents a fermion at rest, since the solution does not...

the following 2nd order differential equation is given: 2y'' + 4y' +8y=8x........(1) i want to find damping ratio, undamped natural frequency, damping ratio coefficient and time constant for the above system. solution: comparimg (1) with general system equaion (veriable can be exchanged)...

$y''+\frac{1}{x}y'=\frac{2}{x^2}-4$ Hey. This is probably really simple but I'm stuck :p how do I approach this?

I'm trying to solve a 2nd order differential equation in matrix form. I'm not familiar with Matlab, and have tried solving this using tutorials on youtube. Initially, theta1 = pi/4, theta2 = 7*pi/12, theta1_d = 0, and theta2_d =0. Time interval is (0,1.2). When I try to solve this using ode45...

Homework Statement A resonance filter is a specific second-order digital system designed to attenuate all frequencies except at and around a given center frequency. The transfer function of a resonance filter is: H(z)=(1 - r)(1 - rz-2) / (1 - 2rcos(ωcT)z-1+r2z-2) where ωc = 2πfc, where fc is...