Separable Definition and 185 Threads

Homework Statement I'm having trouble understanding my class notes from a lecture on separable differential equations. I would like to solve the equation g(y)y' = f(x) The Attempt at a Solution g(y)y' = f(x), G(x), F(x) exists and are continuous The left side is the derivative...

Hi there, I was working on two of my homework problems for calculus and I'm stuck. First equation is: dy/dx=e^(x+y), solving for y So far here is what I have: dy/dx=(e^x)(e^y) therefore dy/dx=(e^x)/(1/e^y) INT(1/e^y)dy=INT(e^x)dx from the integration, my calculator comes up with...

Ok here's my problem: The acceleration of a car is proportional to the difference between 250 km/h and the velocity of the car. If this machine can accelerate from rest to 100 km/h in 10s, how long will it take for the car to accelerate from rest to 200 km/h? Here is what I've done so...

Homework Statement Solve y'=y^2/x , y(1)=1 and give the largest x-interval on which the solution y(x) is defined. Homework Equations The Attempt at a Solution dy/dx = y^{2}/x \int dy/y^{2}= \int dx/x y=1/(1-ln|x|) Therefore, i find intervals (\infty, e), (0,e), (- \infty ...

Hi I've been working on this problem repeatedly and thought I understood how to solve separable equations problems but I keep getting the wrong answer. y' = (1-2x)y^2 Here's what I got for the problem: y'y^2 = (1-2x) \int(1\y^2) dy = \int(1-2x)dx ln | y^2| = x-x^2 + C e^ln|y^2|...

Homework Statement Problem given basically in the beginning of the book, Sec. 1.4, about separable equations. Find general solutions (implicit if necessary, explicit if convenient) of the diff. eq. dy/dx+2xy^2=0 Homework Equations There was a previous section where they popped...

Homework Statement solve the quation dy/dx = (4x - x^3) / (4 + y^3) the first thing the book does is rewrite the equation as: (4+y^3)dy = (4x-x^3)dx and i understand that they are 1st separating it out... BUT shouldn't it be (1 / (4+y^3))dy? How can they dissmiss the fact...

Homework Statement dy/dx =[cos^2(x)][cos^2(y)] Homework Equations The solution to this problem is y = +/- [(2n + 1)*pi]/4 How? Do i just plug C back into the equation? That seems a little messy The Attempt at a Solution dy/cos^2(y) = cos^2(x) dx After integrating...

Homework Statement I'm not sure how to proceed here. The first one asks me to find the area of a surface obtained by rotating the curve y = cos(x), 0 \leq x \leq\ \frac{\pi}{3} The second one asks to Solve: \frac{dy}{dt} = \frac{ty+3t}{t^2+1}\ y(2)=2 Homework Equations The Attempt at...

[SOLVED] Separable Equation with Condition? Homework Statement Solve. http://www.mcp-server.com/~lush/shillmud/int3.71.JPG Homework Equations The Attempt at a Solution I'm not sure how to separate this. Also, since the directions consist of only one word, I'm not sure if y(2)=2 is...

In general topology, how did separable spaces get their name? It is not intuitively clear to me what can be separated in a separable space, so I was wondering what was the history behind that name.

Homework Statement The question is discussing the growth rate of a tumor as it decreases in size (called the Gompertz equation: I am needing so SOLVE THE SEPERABLE DIFFERENTIAL EQUATION. Homework Equations dx/dt = f(t)g(x) =(e^-t)(x(t)) x(o)=1 The Attempt at a Solution 1. I...

Homework Statement y'+ytanx = cos x y(0)=1 Homework Equations The Attempt at a Solution We are studying separable ode's and integrating factor right now, I am a little confused... If someone could steer me in the right direction, it would be greatly appreciated... This is...

Homework Statement \frac{dy}{dx} + x^{2} = x Homework Equations Above. The Attempt at a SolutionAfter rearranging, I am stuck at \int \frac{1}{x-x^{2}} dx = \int dt I can't think of any u-substitution, or any other trick for integrals I could use to solve this.

I am just supposed to find the general solution, in an explicit form if possible. y'=xcos^(2)y Thanks!

Homework Statement 'In topology and related areas of mathematics a topological space is called separable if it contains a countable dense subset; that is, a set with a countable number of elements whose closure is the entire space.' http://en.wikipedia.org/wiki/Separable_metric_space Let...

Homework Statement Suppose that a town has a population of 100,000 people. One day it is discovered that 1200 people have a highly contagious disease. At that time the disease is spreading at a rate of 472 new infections per day. Let N(t) be the number of people (in thousands) infected on...

http://img441.imageshack.us/img441/3306/questionmakaveliec7.gif How do I solve this? I can't seem to get part a and thus any of the other parts... Any help would be appreciated... Thanx! :cool:

Hi, I'm having trouble with this ODE problem: The prompt asks to find the solution of the ODE using separation of variables. dy/dt = (ab - c(y^2)) / a, where a, b and c are constants. I proceed to divide both sides by (ab - c(y^2)) and multiply both sides by dt, but I'm having...

In an investigation of a physics problem, I ran into the following equation: d^2(y)/(dt)^2 = k * y * (y^2 + c)^-1.5 I know how to solve separable first order differential equations but this one seems to be beyond me. Assistance?

dy/dx= (y^2 -1)/x 1. Give the general equation of the curves that satisfy this equation. 2. Show that the straight lines y=1 and y=-1 are also solutions 3. Do any of the curves you found in 1) intersect y=1? My Ans: 1. The general solution i found out to be x^2 + C =...

okay... i got this problem sovle the separable differential equation 4x-2y(x^2+1)^(1/2)(dy/dx)=0 using the following intial condition: y(0) = -3 y^2 = ? (function of x) I guess that means the constant is -3 so i put all the x on 1 side and all the y on one side 4x =...

How would I start this one? I tried dividing by y, but that does not work y'=xy/(1+x²)

Hello, Yes, this is for a class - but it is simply a high school homework assignment. I am solving for v. (This is only part of the homework problem, BTW). http://mlowery.t35.com/AP_4_1a.jpg My question is particularly concerned with the last two lines. On the final line, is the -64/5...

Hello everyone i did this one surley thing it would work out and yet another failure. :cry: Solve the separable differential equation 11 x - 8 y*sqrt{x^2 + 1}*{dy}/{dx} = 0. Subject to the initial condition: y(0) = 6. y = ?I'm pretty sure where I messed up is when i tried to solve for y, i...

I'm almost finished my calculus book (I'm self-teaching) and in the last 2 chapters it's giving a brief intro to differential equations. the second section is for "separable" and I'm stuck on this one halfway through the exercises. It doesn't seem to be separable by any means I can see unless...

Hi, I have just started my differential equations class. To solve the initial-value problem, 8cos^2ydx + csc^2xdy = 0 (initial condition: y(pai/12) = (pai/4) )using separable equations method, I have to change the equation to 8/csc^2dx + 1/cos^2ydy (Am I right so far?) My problem is I...

Hi all, Suppose E/F and K/E are finite separable extensions. Prove: K/F is a separable extension. I tried, but I'm stuck again. (Have you noticed I have one like this every week? And it seems I'm the only one that's even trying to submit these H.W. weekly...). Anyway, that was my...

Suppose k is separable over E. Prove that E(k)/E is separable. A hint, if I may ask. :smile:

Q. Prove that a separable differential equation must be exact. Well, don't know no how to do this. There is no proof given in the textbook. All I know, Mdx = Ndy ( Test for exactness ) Anybody here, any ideas

1) In R3 closure of an open ball is a closed ball, but this may not hold in general metric spaces. Can somebody give an example explaining the above statement? 2) what is a separable space? some good references are welcome. thanks for your help in advance. aditya...

Hi, Please bear with me, I've only had the first sort of "pseudo-lecture" in ordinary d.e.'s this past week, and I was doing some reading ahead. It occurred to me that if linear first-order differential equations are those that can be written in the general form: \frac{dy}{dx} + P(x)y =...

I'm doing some revision on differential equations, and am getting stuck on what should be a simple problem. The question is: Solve: dP/dt = 0.2P(1000 - P) Find particular solutions when (i) P(0) = 1000 and (ii) P(0) = 2000 The answers are supposed to be: i) P(t) = 1000 ii) P(t)...

How can I show that the separable equation dy/dx = M(x)N(y) is also exact? Any ideas? Thanks in advance! -epiclesis

Yesterday Meteor found this new paper of Rovelli's and added it to the "surrogate sticky" collection of links. In case there is need for discussion, it should probably have its own thread as well. The paper expands a key assertion made on page 173 of the on-line draft of Rovelli's book...