Ode Definition and 1000 Threads

y^2=y' \Rightarrow y=\frac{y'}{y} \Rightarrow \int y dx = ln \left( y \right) \Rightarrow y=e^{\int y dx}=e^{\int e^{\int y dx} dx}=e^{\int e^{\int e^{\int y dx} dx} dx}=\cdots Is that correct?

Homework Statement Determine a series solution to the following ODE about x0 = 0: xy'' + y' + xy = 0 The Attempt at a Solution I'll try to keep this concise. I first divided through by x and made the usual guesses for the form of the series. Subbing those in gave...

Hello! I would like to prove the following statement: Assume f\in C^{1}(\mathbb{R}). Then the initial value problem \dot{x} = f(x),\quad x(0) = x_{0} has a unique solution, on any interval on which a solution may be defined. I haven't been able to come up with a proof myself, but would...

Homework Statement obtain the general solution y(x) of y''-2y'+y=e^(2x)/(e^x+1)^2 Homework Equations variation of parameters The Attempt at a Solution I have obtained the continuous equation. I tried two methods of variation of parameters, but both of them got me stuck. 1...

u'u''-k1u=-a*cos(hy)-b where,u'=du/dy; and and a,b,k1 are constants conditions u(-H)=0; u'(0)=0; where 2H is height of the channel where the liquid is flowing please help any suggestions are welcome i couldn't find the analytical soln numerical soln also am havin a dead end so please

R'' + 2rR' - Rl(l+1) = 0, where R = R(r) and l is a constant. This is portion of sol'n by separation by variables to laplace's equation in spherical coordinates. I tried laplace transform, but reached integral that I don't think admits analytic sol'n. F'(s) + F(s)[\frac{1 + l(l+1)}{s} -...

The problem is : (y*e^(2xy) +x) + [ b* x*e^(2xy) ] y' =0. Find b so the equation is exact and solve. I found b=1 and worked the problem to (1/2)e^(2xy) + (x^2/2)e^(2xy) + h(y); where I found h(y) to be simply c. The answer in the text states that e^(2xy) + x^2 =c Would I be...

Can you guys point me in the right direction on the problem below? Solve the given initial value problem and determine at least approx. where the solution is valid: (2x-y)dx + (2y-x)dy= o, y(1)=3 So I have My =-1 and Nx= -1 x^2-xy+ h(y) => -x+h'(y) = 2y-x => h(y)= y^2 => x^2...

Hey, we have to solve the following problem for our ODE class. Homework Statement Find the solution of the initial value problem dx/dt = (x^2 + t*x - t^2)/t^2 with t≠0 , x(t_0) = x_0 Describe the (maximal) domain of definition of the solution. The Attempt at a Solution Well...

Homework Statement yy''=y'^{2}-y'^{3} I'm quite sure I got lost somewhere. Can anyone show me where? Thanks Set z(y)=y' then \frac{\partial z}{\partial y}=y''\cdot y'=zy'' so y''=\frac{z'}{z} Plugging this in y\frac{z'}{z}=z^{2}\left(1-z\right) and so...

Hello all, I don't have much experience with ODEs. I have a simple system, which I believe is first order linear, similar to the following: dA/dt = 2A + 3B - C dB/dt = A + 2B - C dC/dt = -2A + 5B - 2C Now I would like to include the constraint that A + B + C = 1. How do I do this...

2r(s^2+1)dr + (r^4 + 1)ds = 0 2.book answer different than mine...book's answer: r^2 + s = c(1 -r^2 s) 3. 2r(s^2+1)dr =- (r^4 + 1)ds -2r/r^4+1 dr = 1/s^2+1 ds int -2r/r^4+1 dr = int 1/s^2+1 ds with u substitution on left we have u = -2r, etc. tan^-1 r^2 = - tan^ -1 s + c tan^-1 r^2 +...

Can anyone help me solve this ODE: ..in other words, find a general solution? dy/dx = e^(x+y) I use a separation method, but i can't take the natural log of -e^(-y). So, help?

Homework Statement Let's say I have a function for a circle x^2 + y^2 = C where C is a constant. Then this is a cylinder with the z-axis. Now in my ODE book, we would normally define it as F(x,y) = C = x^2 + y^2 as a level surface. Now my question is about what the partial...

Hi, I have a system of coupled ODE like: a1 * Y1" + a2 * Y2" + b1 * Y1 + b2 * Y2 = 0 a2 * Y1" + a3 * Y2" + b2 * Y1 + b3 * Y2 = 0 I know for example by eigenvalue method I can solve it, but here is the issue: Y1 = f1 (x - a) and Y2 = f2 ( x - b). In the other word there is a shift...

Homework Statement the problem is to solve this differential equation: x^2 y'' + xy' + (4x^2 - 1)y = 0

Homework Statement Proof that there exist more than one solution to following equation \frac{dx}{dt} = \sqrt[3]{x^{2}} , x(0) = 0Homework Equations The Attempt at a Solution Well, I need a confirmation to my attempt of solution. The one is quite forward: \Rightarrow x=(1/3(t+c))^{3} Pluging...

I'm reading the differential equations chapter of Advanced Calculus by Loomis, and have some questions. First it proved the following theorem: Let A be and open subset of a Banach space W, let I be an open interval in R, and let F be a continuous mapping from I X A to W which has a...

hello, I have read in a number of papers that if we have a cantilever beam and are only interested in the movement of the tip when the base is being excited at the frequency of the first eigen mode , then the whole beam can be replaced by a spring mass system. Can anyone tell me of a...

Homework Statement \mathbb{x'}= \begin{bmatrix} 1 & 1 \\ 4 & 1 \end{bmatrix} \mathbf{x} \ + \ \begin{bmatrix} 2e^{t} \\ -e^{t} \end{bmatrix} Find the general solution. Homework Equations The Attempt at a Solution Well i found the eigenvalues of the matrix That i'll call...

Hey guys! I'm trying to solve a 2nd order differential equation. I am quite familiar with the method of solving these equations like treat them like characteristic equation ODE. but there's a question which I really want to solve. question is d^2 X/dt^2 +dX/dt +sinX=0. How should I solve this??

So I've been trying to figure this out for a while now and all my attempts have failed, like I tried using the command ODE45 but it did not work... this is the equation -> m(d^2x/dt^2) = −kx − β(dx/dt) I'm given that 2λ = β/m, and and ω^2 = k/m and I must solve for when λ^2 − ω^2 > 0 I...

Homework Statement Hi all came across this problem whilst doing some revision and i can't work out the answer Solve the following equation with laplace transformation Homework Equations y''+16y = f(t) = { 1 t < pi ] with y(0) = 0 and y'(0) = 0 _____________{ 0 t >= pi ]...

Homework Statement Find the general solution to y''-2y'-24y=50e6x-14cos(x)-175sin(x) Homework Equations I can't figure out how to solve for B,C,D, and E. I'm wondering if I did something wrong. The Attempt at a Solution I'm attaching photos, since it'd take forever to type this...

Homework Statement Find the general solution to x3y'''-9x2y''+76xy'=0 Homework Equations I'm kind of confused on where to start. I'd suppose you'd throw in y=emx but I'm not positive since there are Xs in there. Once I know what to do with the x terms, I can just find all the roots and that'll...

We've done a little bit on existence/uniqueness of solutions, and there's one thing that's a little confusing to me. We have a theorem which (paraphrased) says that if you have a linear ODE with an initial value problem, then a solution exists on the largest open interval containing t0 on which...

Homework Statement x^3y'+4x^2y=1/x Homework Equations NA The Attempt at a Solution I've tried separation of variable but I can't get the ys on 1 side and the xs on the other. Please help the exam is soon and I don't know what method to use?

Homework Statement Find the general solution to y\frac{\mathrm{d} x}{\mathrm{d} y} + 2x = 5y^3The Attempt at a Solution I didn't know if they wanted to say x(y) or y(x) So i went with x(y) \frac{\mathrm{d} x}{\mathrm{d} y} + \frac{2x}{y} = 5y^2 Now this is bad because I got \frac{2x}{y}...

Homework Statement My book did this y' + p(x)y = q(x) u(x)y' + u(x)p(x)y = u(x)q(x) Then they did some algebra and product rule manipulation and turned it into a seperatable diff eqtn Now here is my problem, why is it that they can multiply both sides by u(x)? doesn't that change the whole...

Homework Statement [PLAIN]http://img64.imageshack.us/img64/6967/unledyac.jpg 2. The headache I know that f(x,y) is just any function, but my brain completely collapsed when they introduced \frac{\partial f }{\partial y} What does that mean? Why only \frac{\partial f }{\partial y}...

Homework Statement y^{'}+3y=t+e^{-2t} Homework Equations (μy)'=μy'+yμ' The Attempt at a Solution First I found the integrating factor: \frac{dμ}{dt}=3μ which becomes μ=e^{3t} I multiplied through by e^{3t}, yielding y'e^{3t}+3e^{3t}y=te^{3t}+e^{t} I combined the LHS into...

Hi Physics forums. I saw this question in a book, I'm not asking for the answer and this is not a homework, I just don't know how to figure out this: What can you say about a solution of the equation "y' = -(y^2)"just by looking at the differential equation? I checked at the book's answer...

I'm working on this differential equation this few days... Could you give some guidance on approximate solutions to it? i(t) is the only function while all others are parameters. \frac{di(t)}{dt} = -\lambda(\sigma\phi\sqrt{i(t)(1-i(t))} + N\mu i(t)(1-i(t)) Thank you a lot!

Hi, I currently have this problem to solve, and I'm quite stuck. I would much appreciate it if anyone could point me in the direction on how to solve it. This is my go at it, although currently I don't have access to MATLAB until tomorrow as the university library has now closed...

I hope this OK to do, I posted the same question in the science book section and have not gotten a response(admittedly I haven't waited very long but I am sort of in a rush and it doesn't seem to be a question which comes up often). I would like to purchase a book on ODE theory(as in it gives...

Dear all, Homework Statement Draw behavior around (0,0) of solutions to the following nonlinear system \left( \begin{array}{c} x'(t) \\ y'(t) \end{array}\right) =\left( \begin{array}{cc} cos {x(t)} + sin {x(t)} + {x(t)}^2 + {x(t)}^2{y(t)}^3 \\ -x(t) + {y(t)}^2 + y(t) + sin {y(t)}...

Homework Statement This is the solution to an IVP, and the question asks how the function behaves as x Approaches infinity...

Homework Statement So, I have found a general solution to a system of linear first order ODE's and this is what I got: X = c1v1e^(-1+2i)t + c2v2e^(-1-2i)t where v1 = [-1+2i, 5], v2=[-1-2i,5]. The question is, how do I now change this solution into its real equivalent? i.e. I don't want any...

Guys, I have an ODE like this: The following code was used to generate this LaTeX image: \frac{d^2y_{1}}{dx^2} + \frac{d^2y_{2}}{dx^2} + y_{1} + y_{2} = 0 where, y1 (x) =y2 (-x). Do you have any idea how to solve it? Thanks in advance.

Hello, I have a system of two second-order autonomous ODEs arising from a population genetics model: (a-b y)x(1-x) + x''=0 (a-b x)y(1-y) + y''=0 where a and b are constants, and x, y are fonctions of t. Is there any hope to solve this system? Thank you for your help.

Hi all, I was looking at the buckling problem of a piece of paper with both ends clamped. When the two ends come closes they form a bulb-like shape and I was interested in deriving the shape numerically by solving NL ODE, which comes from energy methods (neglecting gravity). The ODE I got...

Find the general solution of x2y'' + xy' + (x2 - 1/4)y = 0 and express it in terms of trigonometric functions. (You don't actually have to solve the equation from a trial function in this problem, but you must identify the differential equation. Then, you may write the solution and prove...

Reduction of Order ODE - Stuck on question! Help Please! The question says that y1= x is a solution to: x^3 y'' + x y' - y = 0 It then says to use y2 = y1 f(x) So I can do it this far and then I just get lost and my notes don't seem to clear anything! I'm just going to say y(2) = y2...

2d2ydx2 + 4 dydx+ 7y = e^−x cos x i solved the equation for yc. but couldn't solve for yp as i dint know what kind of undetermined method to put for yp, particular integral.

Homework Statement i need to create the phase diagram for the equation \ddot{x}=x^{3}-x using MATLAB Homework Equations Well i have worked out that there is a centre point at 0,0 and a saddle point at -1,0. The Attempt at a Solution i found a site on the internet which shows me...

i want to know the general solution of dy/dx - y = x + 2x^2 i don't know how to do it. looked at every book. i can only do it when seperating the variables but here we have "-y"

Homework Statement How do you use the Quadratic Formula to solve First Order ODE? For example, I am given this integration (see attachment at the bottom). Homework Equations The Attempt at a Solution I integrated both sides but I do not know where to go from there (see attachment at the...

I am to find the general solution of the following two equations, using operator notation: x''-3y'-2x=0 y''+3x'-2y=0 The book suggests starting out with: (D^2 -2)x - 3Dy = 0 3Dx+(D^2 - 2)y = 0 but for the life of me, I do not see how they got this from the first two equations.

Homework Statement Find an expression for x(t) and plot on graph T < 0 < 3T v = 4 for t < 0 = 1 for t >= 0T is time const. Homework Equations Voltage across capacitor cannot change instantlyThe Attempt at a Solution Well the transfer equation is \frac{X}{Y}(jw) = \frac{2+jwC}{1+jwC}...

\frac{d\mu }{dt}=-\left( kx\right) \left( \frac{\mu _{m}^{3}-\mu ^{2}\mu _{m}}{\mu ^{2}+\mu _{m}^{2}-2\mu \mu _{m}+\mu ^{2}K_{s}}\right) \frac{dx}{dt}=\mu x Any method for me to solve the pair of nonlinear equations or numerical graph of the differential equation. *\mu_{m} and K_{s} are...