Ode Definition and 1000 Threads

Homework Statement Consider the following initial value problem for two functions y(x),z(x): 0 = y''+(y'+7y)\text{arctan}(z) 5z' = x^2+y^2+z^2 where 0 \leqslant x \leqslant 2,\; y(0)=1.8,\;y'(0)=-2.6,\;z(0)=0.7. Rewrite the system of ODEs in standard form using a suitable substitution...

I need to demonstrate that there are 3 possible nonzero steady states if r and q lie in a domain in r,q space given approximately by rq>4. Could this model exhibit hysteresis? The below ODE is nondimensionalized. $0<\varepsilon\ll 1$ $\displaystyle \frac{du}{d\tau} = ru\left(1 -...

dimensionless ODE $\displaystyle\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\frac{u^2}{1+u^2}$ $\displaystyle U=r-\frac{ru}{q}$ and $\displaystyle V=\frac{u}{1+u^2}$ Show using conditions of a double root that the steady state is given parametrically by $\displaystyle...

Homework Statement y'' + 4y' +4y = 5e^(-2x) y''+9y=2sin(3x) Homework Equations combined with 3 The Attempt at a Solution For the first one, I started off by finding the general solution. r^2+4r+4=0 r=-2, double roots y=c1*e^(-2x)+c2*x*e^(-2x) And then when solving for the...

So I'm supposed to prove that {x}^{.}(t) = x^{2}+ t^{2} with x(0) = 0 blows up before t = 1 . I'm not sure what method to use to solve I've tried setting up an integral such as \int^{x(t)}_{x(0)} \frac{dx}{x^{2}+t^{2}} = \int^{t}_{0} dt but I didn't think I could do this since 't' is...

I am having a problem. I think i went well in decomposing the partial fraction and integrating, however my answer leaves me concerned. please help if i have gone wrong. Solve: dy/dx + y^2 = y. after taking partial fractions, i simplified this to: (1/y + 1/ (1-y) ) dy = dx and i integrated...

I have a general question about how to construct nonlinear ODE systems with given condition such as # of critical points with certain characteristics of the phase portrait of each critical point. I have no problem solving any type of nonlinear ODE system. But to do the reverse order, I have...

Homework Statement For the differential equation, verify (by differentiation and substitution) that the given function y(t) is a solution.Homework Equations y' - 4ty = 1 y(t) = \int_{0}^{t} e^{-2(s^{2}-t^{2})} ds The Attempt at a Solution I attempted to take \frac{d}{dt} of y(t) as usual...

The equation I'm trying to solve is \frac{dy}{dx} = \frac{y^2 - 1}{x^2-1}, given y(2) = 2 The methods I'm somewhat familiar with are separation of variables, integrating factor, and exact. I tried this: \frac{dy}{dx} = \frac{y^2 - 1}{x^2-1} (x^2 - 1)dy = (y^2-1)dx (x^2 - 1)dy -...

Homework Statement (1 - x)y'' + xy' + xy = 0 Find the first 3 nonzero coefficients of the power series expansion about x = 0 if y(0) = -1 and y'(0) = 0Homework Equations The Attempt at a Solution y = \sum^{∞}_{n = 0}c_{n}x^{n} From above, I can say that y(0) = 1 = c_{0} and y'(0) = 0 = c_{1}...

Dear all, I am wondering if anyone knows the solution to the following nonlinear ODE, \left( -3 + \frac{ f(r) f'(r)}{r} \right)(1+ f'(r)^2 ) + f(r) f''(r) = 0 subject to the initial conditions f(R) = f(-R) = f_0. I have a feeling a closed form solution exists to this ODE because I...

Homework Statement dT/dt = -k(T - T_m) T is the temperature of the body, T_m is the temperature of the surroundings, -k is some contant and t is ofcourse time Homework Equations no idea The Attempt at a Solution I tried solving this using first order linear ODE...

Homework Statement The problems are these: y' + (3y/t) = (Sin(t)/t^3) ty'-2y = t^3 + t^2, t>0 (general case) y't^3+(3yt^2), y(2) = 0 (specific case) Homework Equations Basic ODE solving skills The Attempt at a Solution I can't figure out how to make the y's and y''s go on...

Homework Statement So i think i found the general solutions to both these separable equations, but I am not sure if I am suppose to simplify any further to get it in explicit form, and how i can even do that. Homework Equations The Attempt at a Solution 1. \frac{dy}{dx} -...

ODE --What happened to the moth? One theory about the behaviour of moths states that they navigate at night by keeping fixed angle between their velocity vector and the direction of the Moon [or some bright star]. A certain moth flies near to a candle and mistakes it for the Moon. What will...

Let X be continuous a random variable who's support is the entire real line and who's cumulative distribution function satisfies the initial value problem F'(x)=s\cdotF(x)a\cdot(1-F(x))b F(m)=1/2 note that a>0, b>0, s>0 and m is real. m is the median of the distribution, Is it...

Hi. I am new to differential equations. This is probably pretty easy but I don't quite understand how to do it yet. The equation is y^4 -3y'' -4y = 0. I can figure out what class of equation it is. I can write it in the form y'' = F(y), but I am not really sure how to solve it.

Homework Statement Hi everyone, Consider the following system of (first order) differential equations: \dot{x}=f(t_1,x,y,z) \dot{y}=g(t_2,x,y,z) \dot{z}=h(t_3,x,y,z) where \dot{x}=\frac{\partial x}{\partial t_1}, \dot{y}=\frac{\partial y}{\partial t_2}, and \dot{z}=\frac{\partial...

From a cubic function where y(0)=1, y(1)=0, and where there is a local max at y(5/13) I created a basic separable differential equation problem. I wanted to analyze how well different ordered Runge Kutta methods works in an interval [0,1]. Here it is: dy/dt=-6(6/13)1/3(y-343/468)2/3 , y(0)=1...

Homework Statement Solve the following ODE: du/dx=u^2+1 Homework Equations The Attempt at a Solution I have tried making the substitution: u^2=v but this doesn't help. Any hints will be very much appreciated

I'm trying to solve a third-order nonlinear ordinary differential equation. I couldn't get the answer even using Mathematica. The equation is: u'''(t) + u/2 u''(t) = 0 with conditions u(0)=0, u'(0)=0, u(10)=1. I need to get both analytic solution and numerical solution. For the...

Hel(lo, p) I hope you're doing fine I'm stuck with the following: y'' = -1/(y^2) I tried guessing functions (exponentials, roots, trigs... ) , but none worked, I haven't had any DE course, so I don't have specific steps to employ, I appreciate your help, Thanks in advance

Homework Statement For what values of K does the DE xy''-2xy'+(K-3x)y=0 (1) has a bounded solution in (0, \infty)?Homework Equations Not so sure, Frobenius method maybe.The Attempt at a Solution First, I check what happens when x tends to infinity. I see that the DE behaves like \phi ''-2 \phi...

Homework Statement By using the method of differential operators, solve y''+2y'+2y=2e-xsinx 1. Determine what is the annihilator of the inhomogeneous term. 2. Find a particular solution. 3. Write the general solution for the equation. Homework Equations xneaxsin(bx) --> annihilated by...

Homework Statement I must find the constant K such that y''-\left ( \frac{1}{4}+\frac{K}{x} \right )y=0 for x>0 has a non trivial solution that is worth 0 when x tends to 0 and when x tends to infinity.Homework Equations Frobenius method.The Attempt at a Solution I proposed a solution of the...

Homework Statement Solving the linked set of ODEs: y" + y = 1-t^2/π^2 for 0 ≤ t ≤ π y" + y = 0 for t > π We are given the initial condition that y(0) = y'(0) = 0, and it is also noted that y and y' must be continuous at t = π Homework Equations See above. The Attempt at a...

Homework Statement So I had my final exam today in ODE and I had an equation which appeared to be exact, but was not. I also tried to find a special integrating factor to make it exact, but no success. I then attempted to manipulate it into a linear eq, tried separable variables, even...

I have derived a 3rd order non-linear ODE with its respective boundary conditions, and I was hoping to get a hint on how to find a closed form solution to it. The equation is given as: F''' + (1/C^2)*F*F' = 0 Where the primes denote a derivative, and C is just a constant. Any help is...

Homework Statement I have a frequency equation to solve for the displacement for a spring mass damper truss system, as seen below, [m]u''+[c]u'+[k]u=f(t), where m,c,k, are all matrices (2x2), and f(t) is a graph-defined forcing function. I am to use 3 nodes, using the central...

Homework Statement dy/dx + y/x = e^(x^2) Express y in terms of x and arbitrary constant. The attempt at a solution It is in the standard 1st order linear ODE form. P(x) = 1/x Q(x) = e^(x^2) u(x) = x (after calculation) So, d(uy)/dx = uQ d(uy)/dx = x.e^(x^2) I have to integrate both sides...

Hello there, I am interested in the following matter. Given an ODE, can one always find a functional F such that the ODE is its Euler Lagrange equation? I am thinking at the following concrete case. I have the ODE y' = a y I would like a functional given by the intergral over a...

Homework Statement Solve ODE y''-y=e^{-t} y(0)=1, y'(0)=0 Homework Equations The Attempt at a Solution Homogenuous solution t^2-1=0 y=C_1e^t+C_2e^{-t} From y(0)=1, y'(0)=0 y=\frac{1}{2}e^t+\frac{1}{2}e^{-t} How from that get complete solution?

Homework Statement y''-2y+y=xe^xlnx The Attempt at a Solution I don't know what I should do here because lnx. Is it possible to solve this ODE with undetermined coefficients method? how can I solve it?

x''+2x'+x=t+delta(t) x(0)=0 x'(0)=1 The textbook, "Elementary differential equations" by Edwards and Penney, gives the answer as -2+t+2exp(-t)+3t exp(-t) It is clearly wrong, as in this case x'(0)=2, not x'(0)=1.

dc/dx = x^{2}e^{-xc}

i want to solve the following differential equation: y''(x) - A*y'(x) - B*exp(-C*A*x)*y(x) = M*exp(-N*x) A,B,C,M,N are constants. -is there any solution of the above equation (except series solution)? -is there any proper substitution that can turn the variable coefficient into constant...

Homework Statement yy''-y'^2 = y^2lny The Attempt at a Solution well, since the equation is of the form f(y,y',y'')=0 I turn it into the form f(y,p,p dp/dy)=0. After those substitutions are made, we'll have the following equation: yp (\frac{dp}{dy})-p^2-y^2 lny=0 which is a Bernoulli equation...

Where n is a natural number, so we get polynomials of derivatives like \left (\frac{\mathrm{d} y}{\mathrm{d} x} \right )^n + \left (\frac{\mathrm{d} y}{\mathrm{d} x} \right )^{n-1} + \left (\frac{\mathrm{d} y}{\mathrm{d} x} \right )^{n-3}... = 0 Has some ancient greek guy managed to...

Hi, need help solving a first order homogeneous ODE. y'(x)-(a/x)y = b/(x(1+x)^2) Here a and b are some constants. Need to solve this for y. My attempts so far have been to use But this means solving ∫ x^(-a)/(x(1+x)^2) dx which has solutions in terms of Gauss hyper-geometric functions...

Homework Statement Solve using variation of parameters y''' - 2y'' - y' + 2y = exp(4t) Homework Equations Solve using variation of parameters The Attempt at a Solution I got the homogenous solutions to be 1, -1, and 2. So, y = Aexp(t) + Bexp(-t) + Cexp(2t) + g(t) I got...

Homework Statement dx/dt = 2000-500x/100 Solve this linear ODE using integration. You should get a function of t, x(t). This is the "analytical solution". Use the differential equation above, separate the variables, and then integrate to find x(t). Find the integration constant and...

I am having trouble solving this ode, I wasn't sure if this should go under calculus section or differential equations section, but I figured since were given this in calculus 1 it belongs here. We just recently started learning integral calculus and I don't know a whole lot about differential...

I am completely stuck on where to go with the following ODE: (D^4 + 1)y = 0 where D=d/dx I know that trying y=e^(rt) is the obvious solution, however, when you solve this you get r^2 = +-i. At this point I am unsure of what to do becuase if I take the square root of "i" I am unsure of...

Homework Statement Given w'' - w = f(x) w'(0) = 1 w'(1) = 0 Homework Equations Find the Green's Function The Attempt at a Solution The solution to the homogeneous equation is known as: w(x) = A*exp(-x) + B*exp(x) For G's function we have: u(x) = A1*exp(-x) +...

Homework Statement Find all solutions to [dx/dt; dy/dt] = [1, 2; 0, 1]*[x; y] Homework Equations the eigenvalue characteristic equation: det(A-λ*I)=0 The Attempt at a Solution This results in real, repeated eigen values: λ1,2 = 1 for λ1 = 1, (1-1)k1 + 2k2 = 0 choose k1 =...

Homework Statement Hi, I submitted this question on here the other day a user suggested some topics which might help so I have went away and tried this and this is what I have came up with. I just want to know what I have so far is right also I need help with integrating the rhs of the...

I want to solve a set of equations using Python odeint, but output shows me it is wrong. Can you help me? Thanks. Code: # -*- coding: utf-8 -*- from scipy.integrate import odeint import numpy as np from pylab import * import math def func(y, t, k, c, Zr): #px, py...

Homework Statement (4x^3 p^2-2p)dx+(2x^4 p-x)dp=0 The Attempt at a Solution I have no idea how to solve it. It's not an exact differential and It's not of any famous ODE form that. Any ideas would be appreciated.

Homework Statement 2xy'(x-y^2)+y^3=0 Homework Equations The Attempt at a Solution What kind of an equation is that? I first thought that might be a Bernoulli differential equation with respect to x but I failed to convert it that form. I also checked if the equation could have single...

Homework Statement Show that if y1 is a solution to the ODE y'''+a2y''+a1y'+a0y=0 then the substitution y=uy1 reduces the order of the equation to a 2nd order linear ODE. The Attempt at a Solution well, I calculated first, second and third derivatives of y and plugged them in the equation and...