First order Definition and 546 Threads

Homework Statement Solve the following first order differential equation for x, \frac{dy}{dx} = 3xy + xy2 Homework Equations Methods: Separation of Variables, Define an Integrating Factor The Attempt at a Solution I have been staring at this question for a while now, hoping that...

Ok so we are given a word problem discussing compound interest. In the first part of the question, we are given the equation: S(t) = (k/r)(e^rt -1) The next thing we are asked to do is calculate the value of r are given values of k, t, and S(t). The given values are k = 2000, t = 40, S(t) =...

Homework Statement x^{-1/2}(2-x)^{-1/2} 1) approximate to lowest order in x 2) approximate to next order in x Do I apply the binomial expanion? Homework Equations The Attempt at a Solution

Homework Statement Cappy McGreenhorn is looking to buy a new MP3 player. His primary concern is the battery life of the MP3 player. He has decided on either the aPod or the bPod. The percentage of battery life A(t) (after t hours) for the aPod is governed by: (100 - t2)dA/dt + 4tA = 0...

Homework Statement x*u_{x} + y*u_{y}= 1 + y^2 u(x,1) = 1+ x; -infinity < x < +infinity Solve this parametrically and in terms of x and yHomework Equations We are supposed to solve this using the method of characteristics The Attempt at a Solution My problem is that solving the equation...

I am confused by the following example about solving quasilinear first order PDEs. For the part I circled, the solution is just x^2 + y^2 = k where k is an arbitrary constant. To parametrize it in terms of t, can't we just put x = a cos(t), y = a sin(t) ? Here we only have one arbitrary...

Hi, Here is the equation: x+x'=5.1sin(600*t)*u(t) Our teacher gave us a hint that we should try using a substitution which is a system of sines, cosines, and looks something similar to 5.1sin(600*t)*u(t). I tried substituting: x(t)= A sin (w1*t)+B cos (w2*t)+ c cos(w3*t)*u(t)...

Homework Statement Solve the differential equation dx/dt = 0.63 - (9x / 2060). Homework Equations The Attempt at a Solution I started by finding the integrating factor. So I integrated 9/2060, to get 9t/2060. Therefore e^(9t/2060) is my integrating factor. Multiply 0.63 by that integrating...

Homework Statement For the following auto. first order ode: x' = x^2 - y -1 , y' = x + x*y, show that each integral curve begins inside the unit circle remains there for all future time. Homework Equations Okay, i think what needs to be shown... define a new equation r^2 = x^2 + y^2...

I want to solve a first order differential equation on the form y'+y=e^{x} I want to separate the variables, but not sure how...Thanks!

First order linear ODE-integrating factor with absolute value?! Homework Statement Solve the ODE y' + (3/t) y = t3. 2. Homework Equations /concepts 1st order linear ODE The Attempt at a Solution Integrating factor =exp ∫(3/t)dt =exp (3ln|t| + k) =exp (ln|t|3) (take constant of...

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 Find the general solution to the PDE and solve the initial value problem: y2 (ux) + x2 (uy) = 2 y2, initial condition u(x, y) = -2y on y3 = x3 - 2 2. Homework Equations /concepts First order linear non-homogeneous PDEs The Attempt at a Solution I know that the...

"Consider a first order linear PDE. (e.g. y ux + x uy = 0) If u(x,y) is constant along the curves y2 - x2 = c, then this implies that the general solution to the PDE is u(x,y) = f(y2 - x2) where f is an arbitrary differentiable funciton of one variable. We call the curves along which u(x,y) is...

Homework Statement (4y4-9x2y2-144)dx - (5xy3)dy = 0 Homework Equations substitute y = xv dy = dx v + dv x The Attempt at a Solution after substituting i got (4x4v4-9v2x4-14x4)dx - (5v3x4)dx.v + dv.x = (4v4-9v2-14)dx - 5v3(dx.v + dv.x) = 0 = dx(4v4-9v2-14-5v4)+dv(-5v3x)= 0...

Suppose we have a first order linear PDE of the form: a(x,y) ux + b(x,y) uy = 0 Then dy/dx = b(x,y) / a(x,y) [assumption: a(x,y) is not zero] The characteristic equation for the PDE is b(x,y) dx - a(x,y) dy=0 d[F(x,y)]=0 "F(x,y)=constant" are characteristic curves Therefore, the...

Homework Statement Solve the differential equation: y' = 8sin(4yt) ; y(1) = 4 Homework Equations The Attempt at a Solution The integrating doesn't apply because I can't get the equation into: y' + p*y = f(x) form Also, I have tried separating variables, but I can't get the y inside of the...

question : As the salt KNO3 dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation dx/dt = 0.8x - 0.004x^2 if x=50 when t=0, how long will it take for an additional 50g of salt to dissolve. ok, here I'm encountering a...

question : As the salt KNO3 dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation dx/dt = 0.8x - 0.004x^2 if x=50 when t=0, how long will it take for an additional 50g of salt to dissolve. ok, here I'm encountering the...

1. The problem statement. 1. http://img194.imageshack.us/img194/3815/linear.png 2. http://img25.imageshack.us/img25/1543/bernoulli1.jpg 3. http://img23.imageshack.us/img23/7991/bernoulli2.jpg 2.Relevant equations Problem 1 is Linear Differential Equation and Problems 2 and 3...

I have system of first order ordinary diff equations, indipendent variable is x cordinate. I know asymptotic solution in left and right region (i.e. when x->-infinity or x->infinity, e.g. when abs(x)>1000), it's const plus exponentially falling function. I want to find numerical solution in...

Homework Statement The decomposition of AB is first order with a k = 2.3 x 10-7 s-1 at 45oC. If the initial concentration is 0.25 M, the concentration after 2.3 min is: Homework Equations ln[A]t = -kt x ln[A]0 The Attempt at a Solution I have subbed in the values I have but I...

Q: 1) A thermometer requires 1min to indicate 98% of the response to be a step input. Assuming the thermometer to be a first order system, find the time constant. 2)If the thermometer is placed in a bath, the temperature of which is changing linearly at a rate of 10degrees/min, how much...

Homework Statement I have to solve the following differential equation by the "variation of parameters" method.Homework Equations \frac{dy}{dx}x +2y = 3x The Attempt at a Solution The associated homogeneous equation of the initial equation is: \frac{dy}{dx} = -2x^{-1}y So \frac{1}{y}dy =...

I was stumped by this differential equation. The function x = x(t). x^{\tiny\prime\prime} + \frac{1}{t}x^{\tiny\prime} = 0. You have the initial values x(a) = 0 and x(1) = 1. What I did was to introduce a new function u = x', so I ended up with the first order homogenous DE: u^{\tiny\prime} +...

Homework Statement A particle of mass m and spin 1/2 is moving in an infinite, symmetric potential well V (x) = { 0 -L<= x <= L. = ∞ otherwise.. Under the effect of a weak external magnetic field. B = -B k^ ; -L <= x <= 0 = -B i^ 0 <= x <= L...

In my research, I'm using a modified version of the wave equation: \[ c^2 \left( {\frac{{\partial ^2 p}}{{\partial x^2 }} + \frac{{\partial ^2 p}}{{\partial y^2 }}} \right) = - \tau c^2 \left( {\frac{{\partial ^3 p}}{{\partial t\partial x^2 }} + \frac{{\partial ^3 p}}{{\partial...

Homework Statement I have a first order reaction where I need to find the rate constant. I have the following data: T = 30'C the slope of a graph with ln O.D vs T (minutes) is -0.008 so k is 0.008. The Attempt at a Solution I'm unsure about what reaction I would need here. This is...

Homework Statement We recently discussed a problem in class involving free fall and parachutes.One of the examples was to solve for the area of a parachute in drag,gravity,air density,mass and the speed at which the object deployed the parachute and the speed it hit the ground out. I'm pretty...

Is every first order theory with finitely many axioms automatically complete? An axiom schema like that of ZFC's separation counts as an infinite number of axioms.

Hi guys, I have a general problem that I'm not quite sure how to solve. Suppose you have a first order pde, like Ut=Ux together with some boundary conditions. You'd do the appropriate transformations that lead to a solution plus an arbitrary function defined implicitly. How would you know...

OK if we are given the following first order rxn: 2N_2O_5 - > 4NO_2 + O_2 The rate constant is k. Now how would we express the rate law for the decomposition of N_2O_5. - d[N_2O_5]/dt = k[N_2O_5] OR - d[N_2O_5]/dt = 2k[N_2O_5] I think it is the latter but I see all books use...

Do these equations have two general solutions!? e.g. z_x + z_y -z = 0 Using the method of characteristics a=1 b=1 c=-1 d=0 Therefore dx/1=dy/1=dz/z Taking first two terms: x = y + A *Taking last two terms: z = Be^y So general solution is z = f(x-y)e^y BUT if we took first...

I just took an exam and the final problem was the following: dy/dx = (y-3) e^(cos(xy)) y(1)=1 prove that y(x) < 3 for all x for all y that are defined. To be honest, I tried a few things but realized I didn't know where to start. I can show that the limit of the slope from neg...

Homework Statement 10 y′+ 10 y = 7 exp(6*x) y ( 0 ) = 7 Homework Equations The Attempt at a Solution First I divided everything by 10 because the coefficient of the y' should be 1 Then I found the integrating factor, which was exp(integral of 1*dx) = exp(x) = Integrating factor I...

First Order Decomposition -> % of compound. Please help! Homework Statement In a first order decomposition, the constant is 0.00313 sec-1. What percentage of the compound has decomposed after 7.17 minutes? Homework Equations rate = ln[A]o - ln[A]t = kt The Attempt at a Solution I...

First Order Linear Equation I have a question about differential equations... The equation for a general linear differential equation that is: dy/dx + P(x)y = Q(x) So my question is can you have a Q(x) that has both x and y variables? For Example: dy/dx + (1/x)y = (1/x)y^2

Hi. Could someone help me? In Boyd's book nonlinear optics equation 6.2.24 How to solve it? Basically, it is a 4 variables first order partial differential equation. How to solve it analytically? Thanks

Here is the problem. Skip the first two paragraphs to get to the pure math part. There are two cubes of water, both with area of 2 x 2 dm^2. Via the bottom they are connected by a tube, and the flow of water is (surprise, surprise) proportional to the difference in water level between the...

First order differential qusetion [urgent] Homework Statement Question 7 Homework Equations The Attempt at a Solution I can do part a) and i can begin part b, using separation of variables I get: 1/4 ln |1+2v| = ln|x| + C but how do i use this to solve equation I...

Homework Statement \frac{dA}{dt}=\frac{5}{3} - \frac{4A}{150+2.5t} lb/min so basically dA/dt = rate in - rate out Homework Equations This is basically a mixture problem. There is 10 gals/min going in and 4gals/min going out. Tank starts at 150/300 gallons with 1/4 lb/gal mixture. 5gal/min are...

Homework Statement \dot{x}= \cos(t) x_1 +\sin(t) x_2 \dot{y}= \sin(t) x_1 - \cos(t) x_2 Show that the solutions are unbounded. The Attempt at a Solution I tried to find the explicit solution (by hand) but I failed numerous times. What is the right course of action I...

Homework Statement Let a_1,...,a_n be Real. Then define a 2n x 2n matrix A as follows. The following are the first 4 and the last 2 columns; note that the (2k) column equals (a_k)(derivative of the (2k-1) column A[,1] = a_1^(2n),a_1^(2n-1),a_1^(2n-2),...,a_1^(2), a_1 A[,2] =...

Homework Statement Solve the following DE: (6x^{4}+x^{3}+10x^{2}+2x-4)yy' = (y^{2}+y+2)(12x^{4}+2x^{3}+20x^{2}+6x-7) Homework Equations All we really know technique wise is separation of variables then integrate. Basically this is the first week of DE class. The Attempt at a...

What am I doing wrong?? Solving first order DE's Homework Statement Solve the following first order differential equation: ty' + (t+1)y = t; y(ln 2) = 1, t > 0 Homework Equations The Attempt at a Solution I try to solve this using the method of integrating factors. First I...

Homework Statement dy/dx = (2x + y - 1)^2 Homework Equations The Attempt at a Solution Let u = 2x + y du = 2 + dy/dx dy/dx = du/dx - 2 dy/dx = (2x + y - 1)^2 so du/dx - 2 = (u-1)^2 du/dx = (u-1)^2 + 2 du / ((u-1)^2 + 2) = dx 1/sqrt(2) * arctan...

\frac{dx}{dt} = \cos(x+t) I'm having real troubles with this; I tried a substitution of u=x+t but it just ends up as, t=\tan{u} + \csc{u} + C And I can't see where to go from there. (the middle function is cosec; it didn't come out very clearly on my screen).

First Order Linear Non-Homogeneous Equation Homework Statement I need to solve for e(t) Homework Equations Do I use Laplace Transform for the last integral? The Attempt at a Solution \begin{subequations} \begin{eqnarray} \nonumber \dot{\hat{{\cal E}}}(t) &=& -\kappa...

Homework Statement y' = -y + sin(t) Homework Equations y' = \dfrac{dy}{dt} = f(t,y) The Attempt at a Solution The solution should be, according to my textbook, as follows, y(t)= \dfrac{3}{2}e^{-t}+\dfrac{1}{2}\left({sin(t)-cos(t)}\right) I have looked at the various 'typical' forms of...

Homework Statement Solve this differential equation: (y^2 +1)*dx + (2xy + 1)*dy = 0 Homework Equations dy/dx + P(x)*y = Q(x) u(x) = e^(integral of P(x)dx) (d/dx)(u(x)*y) = Q(x)*u(x) y = (integral of (Q(x)*u(x)dx))/(u(x) The Attempt at a Solution I tried dividing by dx then...