Separable Definition and 185 Threads

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 guys, I was working on this problem regarding separable equations and could not solve it.. dy/dx = ay+b/cy+d My work: I reorganized the equation to become dy(cy+d/ay+b) = dx integrating both sides, you get the integral of (cy+d/ay+b) and dx which is a constant k. I'm pretty sure...

Homework Statement If y(1+x2) dy/dx = 2x (1-y2), prove that (1+x2)2(1-y2)=A, where A is constant. Homework Equations Separable equations The Attempt at a Solution Separate the terms: y/(1-y2) dy = 2x/(1+x2) dx Integrating both sides will get: ∫ y/(1-y2) dy = ∫...

Hello experts! I need your point of view about the following, Do you think is there any loss of generality if the arbitrary constant added when a separable equation is integrated is written in the form lnC rather than just C? Do you think this would ever be convenient thing to do? Is...

Dear readers, Let X be the product space of a countable family \{X_n:n\in\mathbb{N}\} of separable metric spaces. If X is endowed with the product topology, we know that it is again separable. Are there other topologies for X such that is separable? Is there a natural metric on X such that X...

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 +...

Homework Statement Suppse dn/dt = 1/10n and n(1)=-2. Separate the differential equation, then integrate both sides. The Attempt at a Solution How do I do this? There is no 't' to 'separate' from the equation. Would it just be: int[1/10n] = int[0t] ?

Homework Statement Find the solution of the given initial value problem in explicit form and determine the interval in which the solution is defined. \[x dx+ye^{-x}dy = 0\] with initial condition y(0) = 1 Homework Equations The Attempt at a Solution I solved the first part...

I have solutions for 2 problems but they are different from the ones my book provides. This may be due to some simplification they chose to do, but I am uncertain. 1) dy/dx = x2/y ydy = x2dx Integrate both sides and you get y2/2 = x3/3 + C My book gave 3y2 - 2x3 = C 2) dy/dx =...

QUESTION: Solve the separable differential equation dy/dx = sqrt(4y+64), Initial Condition: y(4)=9, and find the particular solution satisfying the initial condition. MY ATTEMPT: (dy/dx)^2 = 4y+64 ((dy/dx)^2)-4y = 64 ,/' (((dy/dx)^2)-4y) dx = ,/' 64 dx Is this the right method...

Hi I have to solve the following LSQ problem: min(||Aax-b||2) where A is a known matrix, b is a know vector x is an unknows vector a is an unknown scalar I can solve directly via pseudo inverse ax=inv(A'A)A'b but how can I isolate a from x? Could Separable least square a scheme...

Homework Statement dy/dx = e^ysin^2x/ysecx Stewart 6e 10.3 # 8 Homework Equations The Attempt at a Solution ydy/e^y = sin^2xdx/secx e^-ydy = sec^-1xsin^2xdx Integration by parts u = e^-y du = -e^-y dv = ydy v = y^2/2 ∫udv = e^-yy^2/2 + ∫y^2/2e^-y = y^2/2e^y +...

Homework Statement dy/dz = ycosx/(1+y^2), y(0) = 1 Stewart 6e, 10.3 # 12 Homework Equations The Attempt at a Solution ∫(1+y^2)dy/y = ∫cosxdy -------------- = sinx + C How do I find the integral of this product? Do I use integration by parts?

Homework Statement dz/dt + e^(t+z) = 0 Homework Equations The Attempt at a Solution dz/dt = -e^te^z integral(dz/e^z) = integral(-e^tdt) let u = 1/e^z dv = dz du = -e^-zdz v= z integral(udv) = z/e^z + integral(ze^-zdz)

Homework Statement y' = y^2sinx Homework Equations The Attempt at a Solution dy/dx = y^2sinx dy/y^2 = dxsinx integral(dy/y^2) = integral(sinxdx) Aside: let u = y^2 du = 2ydy dy = du/2y ln(abs(y^2))/2y = -cosx+C integral(du/2y^3) = integral(sinxdx)

Homework Statement dy/dx = (y cos x) / (1+y2) Homework Equations Meh The Attempt at a Solution I've made it to this point: ln(y) + y2/2 = sinx + C. But we can't figure out to solve for y. It seems impossible with the ln(y) hanging around.

Hey.. I ran across some problems and the notation used is a little different from what I've seen before. considering U(x,y)=X(x)Y(y) Sometimes I'll see Uxx for \frac{d^{2}u}{dt^{2}} which equals X''Y Or Ux for \frac{du}{dt} which equals X'Y But what about U'x Is that a redundant way of...

Homework Statement I'm trying to solve this equation: dN/dt = k(10 000 - N(t)) The attempt at a solution dN/10 000 - N(t) = k dt I integrate, and I'm left with: - ln l10 000 - N(t)l = kt +C I raise both sides with e. I don't know what e^- ln(xxx) is so I multiply both...

Problem and Equation: Solve dy/dx=-y/(x^2+y) Put into standard form, this is ydx+(x^2+y)dy=0 The only ways of solving differential equations that I currently know are when they are either linear (which this is not), separable (this is also not), or exact (ditto), and I vaguely know about...

How do you find a solution for: 2tv' - v = 0 The text says it's separable but I'm not seeing it. I'm just learning so extra details are appreciated. Thanks. (this should have been posted in the homework section - but I can't seem to move it there, sorry)

Hi all, I have a first order separable differential equation that I find a little difficult to solve. The question is from an old maths exam paper from my country. The book I obtained it from only has the answer, but I'd really like to know how to obtain the correct general solution. Okay, here...

Haven't done one of these in awhile and I was looking for a place to make sure I was doing it right. Hopefully one of you can take the time to look it over? Homework Statement Find the unique solution of the differential equation (3y^2)x(dy/dx)-x+1=0 for which y(e)=1 Homework Equations...

Homework Statement 1. Prove that if a metric space (X,d) is separable, then (X,d) is second countable.2. Prove that \ell^2 is separable. Homework Equations The Attempt at a Solution 1. \{ x_1,\ldots,x_k,\ldots \} is countable dense subset. Index the basis with rational numbers, \{ B(x,r) | x...

EDIT: I figured out my error, so don't worry about reading through all of this unless you find it an interesting problem[/size] Homework Statement This is Baby Rudin's exercise 2.27: http://img63.imageshack.us/img63/584/fool.png Instead of proving for R^k, I did it for an arbitrary...

stuck on separable equation (algebra prob??) Homework Statement y' = 2x/(1+2y) y(2) = 0 (1+2y)dy = 2xdx integrate both sides y + y^2 = x^2 + c I am stuck trying to put in in explicit form, so y = ... is this completing the square or something? Homework Equations The...

Homework Statement Solve the separable differential equation for u du/dt = e^(6u + 8t) Use the following initial condition: u(0) = 13. Homework Equations Techniques for solving separable differential equations. 1. Group variable and respective dy,dx,dz, etc. together 2. Integrate both...

Homework Statement Find the y-intercept of the curve that passes through the point (4/9,1) and whose slope at (x,y) is −2/y3. Homework Equations The Attempt at a Solution woudnt the y-int be y=-2x/y3 + 5.5 ? i got it by plugging the slope into m in the equation y=mx+b then...

Homework Statement The following is an explanation from my tutorial. I do not understand it. {\frac{d}{dx}(y_1{{y_2}'}-y_2{{y_1}'})+P(x)(y_1{{y_2}'}-y_2{{y_1}'})=0 Overlooking for the moment that P(x) may be undefined at certain values of x(so-called-singular points of the equation), we...

Homework Statement Solve the following equation by separating variables.Homework Equations x2y2y' +1 = yThe Attempt at a Solution I have been able to work through the problem to this point: -1/x + C = int(y2/y-1)dy I am not sure how to integrate the right hand expression int(y2/y-1)dy

Homework Statement The volume V of water in a particular container is related to the depth h of the water by the equation dV/dh below. If V = 0 when h = 0, find V when h = 4.Homework Equations dV/dh = 16 sqrt(4-(h-2)2) V(0) = 0 V(4) = ?The Attempt at a Solution I have not gotten the ODE in a...

Homework Statement Solve dy/dx = exp(x-y) given that y = ln 2 at x = 0Homework Equations None.The Attempt at a Solution Firstly let's get the equation into a form so we can re-arrange the x's and y's, and then re-arrange. dy/dx = exp(x)/exp(y) exp(y)*dy = exp(x)*dx Integrate: exp(y) =...

Hi, I'm looking to show that the metric space of convergent complex sequences under the sup norm is not separable; that is what I assume it is since I cannot find a way to prove that it is separable (I am unable to find any dense subsets). A set of complex sequences convergent to a certain...

So, this is where I am stuck: ln\left(y\right)+y^{2} = \sin{x}+c_{0} I am confrused... :blushing:

Homework Statement A tin organ pipe decays with age as a result of a chemical reaction that is catalyzed by the decayed tin. as a result, the rate at which the tin decays is proportional to the product of the amount of tin left and the amount that has already decayed. Let M be the total amount...

In Example 1.5 of Differential Equations Demystified, the equation is y' +2xy = x, and the author claims this is not separable. Now, what am I missing. I try the following. 1) dy/dx = x - 2xy 2) dy/dx = x(1-2y) 3) dy/(1-2y) = xdx I guess one of those is invalid but I just...

Homework Statement (x + 2y) dy/dx = 1, y(0) = 1 Homework Equations The Attempt at a Solution Problem is, I can't separate it. This might be a homogenous type? If so, how would I make it into the g(y/x) form. Thank you.

Homework Statement -y + xy' = 0 and y(2)=5 The Attempt at a Solution This first part trips me up. I am supposed to find the perfect derivative, which is (xy') = 0 ? Is this legal, or does the -y not allow for that? If that is correct, then I know that I integrate that, which...

So, here's the problem: \frac{dy}{dx} = \frac{8y}{5x} To start off, I separate the integrals, which gives me: \frac{dy}{8y} = \frac{dy}{5x} After that, I integrate both sides, which gives me: \frac{ln8y}{8} = \frac{ln5x}{5} + c Now, the question says that it runs through (4, 1), so that...

Homework Statement \frac{dP}{dt}=P-P^{2} It seems that Partial Fractions should be used to solve this D.E., but I cannot find an example to go by. I even tried to rewrite the equation as: \frac{d}{dx}Y\left(x\right)=Y\left(x\right)-Y\left(x\right)^{2} But, that isn't helping me...

Homework Statement \frac{dy}{dx}+2xy^{2}=0 I am stuck on this. I realize that this is a non-linear exact equation, but I just cannot wrap my mind around any type of method to attack this one. TIA for any help

I have tried to solve the differential equation y'=x\sqrt{y} like this: y^{-\frac{1}{2}}y'=x \int{y^{-\frac{1}{2}}}dy=\int{xdx} y^{\frac{1}{2}}=\frac{x^2 +C}{4} y=\left(\frac{x^2+C}{4}\right)^2 Is this the right way to solve it? Because the answer in my textbook says that the...

Homework Statement Is the following separable? http://img90.imageshack.us/img90/3925/separable.th.jpg how do I know if it is? Homework Equations The Attempt at a Solution

Homework Statement dx/dy=-0.6y y(0)=5 Homework Equations The Attempt at a Solution I tried solving it by \intdy/y=\int-0.6dx ln(y)=-0.6x+c ln(y(0))=-0.6(0)+c ln(5)=c ln(y)=-0.6x+ln(5) y=e^{-0.6x}+5 But its incorrect. I don't know what I am doing wrong. Can someone helping...

Homework Statement Find the general solution, y 2ty dy/dt = 3y^2 - t^2Homework EquationsThe Attempt at a Solution I probably have to separate the equation and get y's one side in order to solve, but I'm stuck as to how to separate it. I tried letting u = y/t, so then du/dt = (t dy/dt -...

Homework Statement Solve the separable differential equation \frac{dx}{dt} = \frac{6}{x} , and find the particular solution satisfying the initial condition x(0) = 7. x(t) = . Homework Equations \[ \frac{dy}{dt} = ky \] The Attempt at a Solution lnx=6 x=e^6

What is your definition of separable? For a physical system to be separable, what rules should be applied to define whether a given system is separable or not? Note that if a system is non-separable, we can claim it is ‘holistic’ and therefore capable of producing some unique (emergent)...

So if you have a 3D Shrodinger Equation problem, what allows you so assume that the wave function solution is going to be a product of 3 wave functions where each wave function is for a different independent variable? And also is it true that in general in these cases the eigen-energies are...

Homework Statement Solve the equation for b. db/dx = (e^2x)(e^2b) -- therefore: db / (e^2b) = (e^2x)dx Also note that b(0) = 8. Homework Equations The Attempt at a Solution Following a list of steps my teacher gave me to solve these: 1) Integrate both sides. -0.5...

Hi, I am a little bit confused about singular solutions and their relationship with IVP's and decided to ask you. As far as I understood, the IVP's could be in a form: y' = f(x,y) y(x0) = y0 To obtain a general solution, we could use separable eq. method. I have learned that...

Find the general solution of: x.du/dx - (1/2).y.du/dy=0 I know that for it to be separable u(x,y)=X(x)Y(y) so: x.Y(y)dX/dx + (1/2).X(x)dY/dy = 0 which cancels to: x/X(x).(dX/dx) = - y/2Y(y).dY/dy so: X(x) = -c. Y(y) c is some constant so: x/X(x).dX/dx = c...