Ode Definition and 1000 Threads

Homework Statement dy/dx + 0.8 y = 0.6 e ^-(0.6+0.8) , y(0) = 1 Solve this ordinary differential equation subject to the given condition using exact methods and evaluate the solution y for x = 0.0 (0.05) 0.5, i.e from x = 0 to x = 0.5 in steps of 0.05). Hi, am pretty...

Homework Statement y' = e^{x-y'} The Attempt at a Solution I have no idea how to handle the situation when y' is appeared in the input of a transcendental function. I substituted y'=p to try to find a parameterized solution to this ODE but it leaded me to nowhere.

This is the ODE: y' + siny + xcosy + x = 0. The problem is: Find an integrating factor for the ODE above. You can see my solution to the ODE here: https://www.physicsforums.com/showthread.php?t=543662. from my solution it seems that e^x(sec^2(y/2)) must be an integrating factor. but I fail...

hi suppose we have this equation : d/dt(X)=A(t)*X x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients. coefficients of equations and consequently A are depend on t which is time. how i Solve this equation ? thanks

My school requires Calculus III before DEQ, though I had the department allow me to take the two concurrently. I am wondering what Calc III topics I should be fluent into prepare for Differential Equations. I'm sure this university teaches DEQ with an understood previous knowledge in...

L is the operator. Lx=x'(t)+u(t) x(t) =0. Provided that x(t0)=x0. Before writing the matrix. The book express it out in equations. x(t0)==x0 x(t1)-x(t0)+Δt u(t0) x(t0)==0 x(t2)-x(t1)+Δt u(t1) x(t1)==0 ... Euler's method is x(t0)+Δt f[x0,t0], right? so where did the x'(t) from the...

Homework Statement y' + siny + xcosy + x = 0 The Attempt at a Solution well, I've used Weierstrauss substitutions: siny = 2t/(1+t^2) , cosy = (1-t^2)/(1+t^2) , dy = 2dt/(1+t^2) where t=tan(x/2). 2/(1+t^2)dt + 2t/(1+t^2)dx + x(1-t^2)/(1+t^2)dx + xdx = 0 2dt + 2tdx + x(1-t^2)dx +...

Homework Statement 2y(1+x^2\sqrt{y})dx + x(2+x^2\sqrt{y})dy = 0 The Attempt at a Solution well, I substituted x^2√y=u but then when I tried to differentiate it I understood it would be so hard. Please check and see if I've differentiated it correctly: √y = u/x^2 -> y = u^2.x^-4 -> dy/dx =...

d^{2}u/ds^{2}= cosu[(du/ds)^{2} - k^{2}]

Homework Statement y'=(1-y)(3-y)(5-t) Homework Equations find equilibrium solutions of ODE and determine their stability The Attempt at a Solution equilibrium solutions are y = 1 and y = 3, I'm not sure how to determine their stability without some form of a slope field, is it...

Homework Statement solve y(xy+1)dx + x(1+x^2y^2)dy=0 The Attempt at a Solution well, I substituted u=xy. Here is what I've done so far. du = xdy + ydx -> xdy= du - ydx -> xdy = du - (u/x)dx (u/x)(u+1)dx + x(1+u^2)dy=0 (u/x)(u+1)dx + (1 + u^2)(du - (u/x)dx)=0 (u^2/x)dx + (u/x)dx +...

Hi friends, I have been trying to solve the ode of second degree below with respect to z: d2y/dz2=(i/a*z+b)*y i is the complex i, a and b are constants i ended up with the summation of bessel functions of first end second kind. Then I checked with MATLAB ode solver it gives no...

Hi friends, I have been trying to solve the ode of second degree below: d2y/dz2=(i/a*z+b)*y i is the complex i, a and b are constants i ended up with the summation of bessel functions of first end second kind. Then I checked with MATLAB ode solver it gives no explicit solution...

I am a junior in high school taking AP Calc AB. This is the highest level of math offered at my high school (everyone else in my class is a senior) I want to start taking math classes at my community college. Currently I take College Chemistry I there (fall semester) and it's going very well...

[PLAIN]http://img440.imageshack.us/img440/7352/11unled.jpg Having some trouble. I am not sure what d_t(u) and :u(with the . above it) means. Would appreciate some help. Thanks

Here's my question: as soon as I learned Quantum Mechanics and Schrodinger equation, I saw a "similarity" with the equation one gets in classical mechanics for the evolution of a function in phase space. In QM one has: i\hbar\frac{d}{dt}\psi = \hat{H}\psi and this is a evolution...

Okay, kind of a silly question...but what do all of these stand for? ODE=Ordinary Differential Equations ( ;O I hope this is right, I took a course on this stuff) PDE=Partial Differential Equations ( Hope this is right too, taking this next semster) DDE=...? SDE=...? DAE=...

i have the first solution y_1(t) = t for (1-t)y'' + ty' - y = 0. I need to get the 2nd linearly independent using Abels theorem. the integration is messy but i have it set up (sorry no latex); y_2 = (t) * integral to t ( 1/s^2 * exp( -integral to t (s(s+1) ds) ) ds. Could anyone...

i have this differential equation of the first order [x^2+y^2]+[2xy+y^2+(x^3/3)]dy/dx=0 i tried to solve it by substitution putting x^2+y^2=v ,but it doesn't work also it is not exact or homogeneus to solve it by these methods. I still believe it can be solved using substitution but i can't...

Homework Statement Find a particular solution. 1. y'' +4y = 4 cos (2t) (for this problem, the instructions tell me that the forcing term is a solution of the associated homogeneous solution) 2. y'' + 16 y = 3 sin (4t) Homework Equations The Attempt at a Solution 1. I guess...

Homework Statement Solve 2*dy/dx - y = e^x at y(0) = 0 The Attempt at a Solution So the integrating factor is e^-x Multiplying through by e^-x: 2e^-x(dy/dx) - ye^-x = 1 Now this is where I'm having a slight problem, isn't the left hand side meant to contract via the product...

If I solve a simple 2nd order ODE using a Fourier transform, I only get one solution. E.g.: \frac{d^2f}{dx^2}=\delta (2\pi ik)^2\tilde{f}=1 \tilde{f}=\frac{1}{(2\pi ik)^2} f = \frac{1}{2}xsgn(x) However, the general solution is f = \frac{1}{2}xsgn(x) + Cx + D Why do I...

Hi, I seem to have forgotten some of my math how-to, as I haven't done this in a while. Looking through my notes, Bird, Stewart and Lightfoot, Greenberg, etc. don't really help. My equation is this, at steady state: 0 = 1/r^2 ∂/∂r (D*r^2 ∂C/∂r) + P Where P is some production rate...

I need to derive the solution for the differential equation analytically: y'' + g(t,y(t)) = 0 y'(0) = z_o y(0) = y_o I know the solution is: y(t) = y_o + z_ot - single integral from 0 to t of (t-s)g(s,y(s))ds I believe I need to assume something about the solution being a function...

Find a particular solution for the following non-homogeneous dieren- tial equation by the method of undetermined coefficients: a. y'' + 8y' +12y = e^-2x + sin(2x) b. y'' + 11y' - 12y = 3x^2 + 4 + e^x I got for a. Yp(x) = 1/4xe^-2x + 1/40cos(2x) +1/20 sin(2x) b. Yp(x) = -1/4x^2...

Just started Engineering Math III and have a question. Sorry about the notation, our library computers have scripts disabled. My math prof does a poor job of explaining the concepts. Help me out! Homework Statement Verify the indicated function y=phi(x) is an explicit solution of the...

Homework Statement Find the following IVP Diff.Eq. xyy'=x^2+3y^2 y(1)=2 Homework Equations The Attempt at a Solution I've been struggling with this problem for a while now. I believe I have figured out it is homogenous, thus y=ux substitution applies. Through some work I have arrived at...

Homework Statement Solve the Cauchy problem: (t2 + 1)y' + etsin(t) y = sin(t) t2 y(0) = 0 Homework Equations y'(t,y) + p(t)y = g(t,y) Integrating factor e(integral of p(t)) The Attempt at a Solution I tried finding an integrating factor, but it came out ugly. I couldn't solve the...

ODE, bernoulli equation --> leads to crazy integral ! Homework Statement An Initial Value Problem, ODE (Bernoulli equation) ODE: [x^2]*y' + 2*[x^3]*y = [y^2]*(1+2*[x^2]) IV: y(1) = 1/2 Homework Equations general form of Bernoulli's equation: y' + a(x)y = b(x)*[y^n] First...

Hello everyone, I am working on a project on basically about ODE and phase plane and I am working on this paper by Hanski http://www.arctic-predators.uit.no/biblio_IPYappl/HanskiNature93%20mustelid%20predators.pdf How do i find numerical solutions which methods should I use ...

[SOLVED] simple ODE problem, Bernoulli's Equation Homework Statement Initial value problem: Relation: t*y' - 2*[t^2]*sqrt(y) = 4*y Initial value: y(1) = 4 Homework Equations general form of Bernoulli's equation: y' + a(t)y = b(t)*[y^n] First order, linear ODE form: y'...

Homework Statement Solve the initial value problem: y'+\frac{4y}{x+8}=(x+8)^{8} , y(0)=8. The differential equation is linear. Homework Equations N/A The Attempt at a Solution I can see that the equation is in the form y' +P(x)*y = Q(x) so I'm like "easy, let me get an...

Homework Statement I haven't done this for several years and have forgotten. Kicking myself now over it since it looks like something so simple but i cannot figure it out... I need to break this second order ODE into a system of first order ODE's in matrix form to use within a crank...

[SIZE="4"](xy2+y2)dx + xdy = 0 the questions are: a. Show that the equations above can be an exact differential equations! b. Determine its solutions! Help me please because i have working on it for 3 hours and i can't find its integration factor to change the un-exact differential...

Homework Statement Solve \frac{dy}{dx} - 2y = x^{2}e^{2x} The Attempt at a Solution Integrating factor = e^{2x} So we multiply through the given equation by the integrating factor and get: e^{2x}\frac{dy}{dx} - 2e^{2x}y = x^{2}e^{4x} Contract the left-hand side via the chain rule to get...

Homework Statement i)write down the general form of a semi lenear first order pde in the unknown u(x,y) ii)write down the ode satisfied by a characteristic curve in the x-y plane for your pde ii)give a careful derivation of the ode satisfied by u(x,y) along such a charcteristic curve...

The question is x^2dy/dx + y^2=0 , y(1)=3 I re-arrange the equation to get -1/y^2dy=1/x^2dx Seperated them, then I integrate both sides to get 1/y=-1/x + c Now I don't get how they got the answer y=3x/(4x-3), as when I try use the condition I get a different answer, could anyone help? I...

Homework Statement y''+(1/y)*(y')2=0 Homework Equations The Attempt at a Solution This is another problem I am having trouble with. I have done searches around the internet, but seen that all "non linear" ODE of second order involves a non linear form in a non differential term...

Homework Statement Obtain general solution: x^2 y''(x)-2 x y'(x)+2 y(x) = x^2+2 Homework Equations Using Euler Cauchy method, and using variation of parameters The Attempt at a Solution Hey all, I have been struggling with this problem since yesterday in obtaining the...

Homework Statement Consider a mechanical system describe by the conservative 2nd-order ODE \frac{\partial^{2}x}{\partial t^{2}}=f(x) (which could be non linear). If the potential energy is V(x)=-\int^{x}_{0} f(\xi) d \xi, show that the system satisfies conservation of energy...

Hi there. I have this exercise in my practice for differential equations, and it asks me to find the curve that satisfice for every point (on the xy plane) the distance from (x,y) to the points of intersection for the tangent line and the x axis, and the normal with the x-axis remains constant...

Hello, I need to solve numerically an equation of the form v(t) = k1*z(t)*w(t)-k2*i(t)-k3*di(t)/dt The issue is that rungekutta methods are useful for solving di(t)/dt = 1/k3 * [ k1*z(t)*w(t)-k2*i(t)-k3*-v(t) ] but I need to solve for v(t) What I did was: v...

Homework Statement I'm teaching myself the Green's function method for ODEs, because it looks relevant to my interests. This is a (slightly contrived) problem I just came up with arbitrarily: y''+5y'+6y=sin(x) \; \; \; ; \; \; \; y(0)=y'(0)=0 Homework Equations i) When considered as a...

So the question is y" - y' - 6y = e^-x + 12x, y(0)=1,y'(0)=-2 First I found the general solution which came out to be, Ae^3x + Be^-2x I then Substituted y=ae^-x + bx + c y'=-ae^-x + b y"=ae^-x Then I just compared the coefficients to get a=-1/4, B=-2 and C=-1/6 So I am getting y =...

Determine the general solution to the ODE: y'' + 2y' = 1 + xe-2x I know the solution will be of the form y = yh + yp. The homogeneous solution is y = c1 + c2e-2x. For the particular solution, I have been using the method of undetermined coefficients. c3e-2x won't work as it is not...

Homework Statement assuming dy/dt = Dy, d^2y/dt^2 =D^2, etc: determine the general and particular solutions to the following linear pair of differential equations: 2D^2y-Dy-4x=2t 2Dx-4Dy-3y=0 Homework Equations The Attempt at a Solution I have went through algebraic...

Hello, I'm trying to (numerically) solve the equation y''*y=-0.5*y'^2 in Mathematica. I know there's an analytic solution (and I know how to calculate it), but I want to modify this equation and thus need to verify that the numerical solution for the original equation is exact. I'm using...

I'm trying to solve the following ODE: ydx+(\frac {e^x}{y}-1)dy=0 I tried to transfer this ODE into exact form but no luck. Will appreciate any help.

Homework Statement Find the particular solution to the ODE y"+y=x using power series Homework Equations y=\sum(a_{n}x^{n})The Attempt at a Solution i tried plugging in y=\sum(a_{n}x^{n}) into the original equation and comparing coefficients of x to the first degree, but i am not sure how to...

I've made a lot of simplifications to a Joule-heating problem I'm working on. I'm struggling to solve the following one-dimensional, one variable ODE: Txx + aT = -b with boundary conditions T(x=0) = Ts (Dirichlet) Tx(x=L) = 0 (Neumann) I've learned that this is a non-homogeneous...