First order Definition and 585 Threads

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...

Hi, I am stuck on the initial steps of this problem - its been a while since my diff. eq course. I need to reduce this into a system of three equations then apply a 4th order runge kutta method to solve. Homework Statement f'''+f*f''=0 Boundary conditions: f'(0)=f(0)=0 f'(infinity)=0 A...

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...

Hi, I've come across this equation in my research, and I am so far unable to solve it. The equation is: \frac{dV}{dt} + \frac{1}{RC}V - \frac{I}{C}e^{(-V/n)} = \frac{V_f}{RC} - \frac{I}{C} both terms on the right-hand-side are constants; throughout the equation R, C, I, n, and Vf are...

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...

y'(t) - ay(t) = 0 What is the form of the solution? C \cdot e^{at} ?I have this ODE: T'(t) - (1 - \frac{n^2}{4})T(t) = 0 If I'm right, the solutions should be of the form C \cdot e^{(1- \frac{n^2}{4})t} My book, however, says C \cdot e^ {1- \frac{n^2}{4}t} Who's right?

Homework Statement Solve: (2t+x) dx/dt + t = 0Homework Equations y' +p(X)y = q(x) and y(x) = (\intu(x)q(x) + c)/u(x) where u(x) = e\intp(x)dx Note this u(x) is 2 to the power of the integral of p(x) The Attempt at a Solution (2t+x) dx/dt + t = 0 becomes: dx/dt + t/(2t+x) = 0 by dividing...

Homework Statement Hydrogen peroxide undergoes a first-order decomposition to water and O2 in aqueous solution. The rate constant at 25°C is 7.40e-4s. Calculate the volume of O2 obtained from the decomposition reaction of 1.00 mol H2O2 at 25°C and 740 mmHg after 12.4 min. Homework Equations...

Homework Statement http://i.thespiffylife.com/files/1/trans1.jpg i have to find Vc(t) Homework Equations I know that Vc(0+) = Vc(0) = Vc(0-) and Vc = Vs*e^(-t/RC) The Attempt at a Solution What I'm unsure on is what the equivalent resistance of the circuit would be so I could find the...

Homework Statement Does the following differential equation have a simple analytic solution? \frac{dy}{dx}=y-\frac{2x}{y} Homework Equations Don't know. The Attempt at a Solution I would have said that there is no simple solution to this equation, I tried to find the integrating factor...

Homework Statement x(\theta)= x tanθ−cosθHomework Equations The integrating factor is (note it should be negative tan, but the latex won't display it); I= \int -tan \theta\ d \theta The solution is given by; x \ e^{I}=-\int \ e^{I}*cos\theta\ d \theta The Attempt at a Solution I=\int...

Not sure if I should have put this here or in the homework section but I am simply asking for direction on these problems. I have 5 problems to work on and my biggest problem is identifying what method to use to find the answer. I don't need help answering because it's something I'd like to...

Homework Statement A 14 lb weight attached to the end of spring stretches it 4 in. Find the equation of motion if the weight is released from rest at a point 3 inches above equilibrium position Homework Equations F=kx mx''+kx=0 The Attempt at a Solution ok I need some help just...

1. y' = a*(y^n) + c a, n and c are constants. Any idea about this problem ? How can it be solved ? i think there is no analytic solution thanks for your help in advance

I have an infinite potential well with length L. The first task was to calculate the eigenvalues and -functions for the energy of a particle in the well. The requirements were \psi(0, L) = 0 and there is no time-dependence. I've calculated: \hat{H}\psi(x) = E\psi(x) E =...

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...

Is the statement -1<1/0<1 decidable using the ordered field/real number axioms and first order logic? I have tried to prove that the statement is either true or false but have had no success since the axioms and theorems only make statements about objects that exist and do not give any clear way...

Ok, so I can get through most of this but I can't seem to get the last part... Here is the problem xU_x + (y^2+1)U_y = U-1; U(x,x) = e^x Characteristic equations are: \frac{dx}{x} = \frac{dy}{y^2+1} = \frac{dU}{U-1} Solving the first and third gives: \frac{U-1}{x} = c_1 The...

Homework Statement Ok, so I can get through most of this but I can't seem to get the last part... Here is the problem xU_x + (y^2+1)U_y = U-1; U(x,x) = e^x Homework Equations The Attempt at a Solution Characteristic equations are: \frac{dx}{x} = \frac{dy}{y^2+1} =...