First order Definition and 585 Threads

Hi, I have the differential equation \left(\frac{df}{dr}\right)^2-\frac{1}{r-1}\left(1+\frac{1}{4r^3}\right)=0, does anyone know how to attack this? (I'm led to believe this is only possible if r>1, not sure why not r<1, although I can see it does blow up at r=1) thanks

Homework Statement Convert the equation to a first order system. d^2y/dt^2 + 3dy/dt + 2y = 0 The Attempt at a Solution Set d^2y/dt^2 = dv/dt dy/dt = V So, I now have: dv/dt + 3v + 2y = 0 Now, I'm not sure what to do with that Y, In my notes we only did examples with...

http://img39.imageshack.us/img39/2991/captureucm.jpg Attempt to solve: omega = 1/R2C1 ; omega = 2pi*f so C1 = 1/R2*2pi*f , where f = 1000Hz so C1 = 0.53 nF (nanofarads) then Ao = -R2/R1, so absolute value is 15 gain V/V? in terms of dB its approx 23.52dB using 20 log X...

Homework Statement I need to resolve this network and find the equation for voltage at some time, t'>0. I know how to find the equation, but I'm having trouble finding the value for tau because I'm not sure what the equivalent resistance is. Homework Equations tau = R*C R1 = 4 k...

Homework Statement What subsets of the real line R are definable in (R,<)? What subsets of the plane RxR are definable in (R,<)? Homework Equations A subset is definable if there is a formula in first order logic that is true only of the elements of that subset. For example, in the...

Homework Statement dy/dx=y-e-x Homework Equations none The Attempt at a Solution According to Wolfram Alpha the solution is y = cex+.5e-x . I tried multiple approaches, but I cannot obtain this answer. I can't figure out what step 1 is. I tried factoring out e-x from the right...

I am trying to solve a problem (not homework, too old for that! lol!) which involves the time dependent schrodinger equation for magnetic moment in time-dependent magnetic fields. I end up with the following that needs to be solved: x' = -i*(b*t-a*t^2)*x - i*c*y y' = -i*c*x -...

dv/dt=g-(k/m)*v^2 i thought about all sorts of diff eq solving techniques but nothing comes up to my mind dv/(g-(k/m)*v^2)=dt but it doesn't really help ...

Homework Statement The equation for the velocity of a falling parachutist can be computed by, v(t) = \frac{gm}{c}(1-e^{-(\frac{c}{m})t}) Use a first-order error analysis to estimate the error of v at t = 6, if g = 9.8 and m = 9.8, c = 12.5 plus or minus 1.5. Homework Equations...

Homework Statement Solve the diferential equation: dx/dt + Rx^2 + G = 0 G constant = 10^18 R constant = 10^-10 Initial conditions x(0) = 10^8Homework Equations what approach to take? The Attempt at a Solution First I try to apply bernoulli, but since in this equation I do not have a term...

Homework Statement t^2 y' + 4ty - y^3 = 0 Homework Equations Hint was given in the question: substitute with v = y^-2 The Attempt at a Solution Dividing by t^2 and isolating y': t^2 y' = y^3 - 4ty y' = y^3 / t^2 - 4y/t dv/dt = 0 y = v^(-1/2) dy/dt = (-1/2)v^(-3/2) v' so...

find the solution for the following equation: dy(t)/dt + 3y(t) = x(t-2), t > 0 and y(0) = 0 i did it by parameterization but am unsure if it is correct. i need help especially with the limits of integration. y' + 3y = x(t-2) yh' = -3yh yh = Ce^-3t y(t) = v(t)e^-3t (ve^-3t)' =...

Homework Statement Going over and over the perturbation theory in various textbooks, I feel that I've NEARLY cracked it. However, in following a particular derivation I fail to understand a particular step. Could anyone enlighten me on the following? Multiply |\psi^{1)_{n}>...

Could anyone help me with this? Donald and Daisy Duck took their nephews, age 4, 5, and 6, on an outing. Each boy wore a tee-shirt with a different design on it and of a different color. You are also given the following information: ■ Huey is younger than the boy in the green tee-shirt. ■...

Some really basic questions about first order DE, which I can't seem to get. What is the difference between a linear and non-linear first order differential equation? For example: dy/dx = cos y dy/dx = cos x And if it's a non-linear first order DE, how do you tell whether it's...

Homework Statement 11(t+1)dy/dt-7y=28t y(0)=13 Homework Equations The Attempt at a Solution I got µ(x)=1/(t+1)^(7/11) and then used 28/11(t+1)^(7/11)*integral of t/(t+1)^(18/11) dt. And that's where I'm stuck.

Homework Statement Hi, If x^2+1=y/(x-y'), where y'=dy/dx, find dy/dx I have tried so many ways, but I cannot seem to get the correct answer. The answers I have got previously are: i) x² + 1 = y/(x - y') (x² + 1)(x - y') = y x(x² + 1) - y'(x² + 1) = y x(x² + 1) - y = y'(x² + 1)...

I was given the following question Which of the reactions on the right are allowed by first-order processes? For those which are not allowed, state one conservation law which is violated. What is a first order process in particle physics? i.e what does first order refer to? What would be...

Having a bit of trouble, what do i do next? Thanks.

The equation of motion of a rocket with mass depletion during ascent and subject to drag forces can be written as M(t) dV/dt = A - M(t)g - BV^2 (Eq. 1) with initial condition V(t=0) = 0 (V is velocity and t is time) Let us assume a linear mass depletion according to...

A question, if you have a nonhomogenous first order differential equation, can it be solved by using the usual nonhomogenous way, with the arbitrary constants, instead of using the integrating factor?

Homework Statement The initial mass of fish in a lake was 7 thousand pounds on January 1st, 2001. Since the time, there was a 4-year moratorium on the harvesting on this specific type of fish. This species of fish reproduce at a rate proportional to the mass and by next year on the same...

Consider cylindrical coordinates p = (x^2 + y^2)^.5  angle = arctan(y=x). Consider your curve to be specified by z(p). Write down a (first order) differential equation governing z(p) please help!

I must derive the 1/4th life expression for a first order rxn. ln(\frac{[A]_{\circ}}{[A]_{t}})=kt ln(\frac{[A]\circ}{\frac{1}{4}[A]_{\circ}})=kt_\frac{1}{4} ln(4)=kt_{\frac{1}{4}} do I set t=1/4 ? \frac{ln(4)*4}{k} \frac{5.545}{k} What am I doing wrong here? The answer is allegedly...

Consider a certain linear system of 2 equations x'=Ax. Suppose the real-valued coefficient matrix A has r=-1+4i as one of its eigenvalues, and that one of its corresponding eigenvectors is (2, 5-2i). Find the particular solution that satisfies the initial condition x(0) = (-4, 3)...

first order system DE --> second order Homework Statement Find a second-order DE for x alone that is equivalent to this system. Homework Equations dx/dt = 2x-y dy/dt = -x The Attempt at a Solution I honestly have no clue where to start; in class we pretty much only stuck to...

Hey, I'm studying Predicate Logic at the moment and I can't seem to wrap my head around the way that english sentences would convert into second order logic. What kind of sentence can be faithfully represented in PL2 but not in PL1? Sorry if this isn't the appropriate section; I'm actually in...

Homework Statement (x+y)dx-(x-y)dy=0 Homework Equations The Attempt at a Solution The solution is c=arctan^-1(y/x)-(1/2)*ln(x^2+y^2) but I don't know how to get the answer. If someone could explain how to solve the above DE, that would be great.

Homework Statement Background: Jack's wife Jill, mindful of the water restrictions is determined to carry buckets of bath water out of the house to water bean stalks. She carries out 18 litres of water on the first day. The amount of water Jill carries out An, in litres on the nth day is...

Homework Statement dx/dt = x - y + (x^2) - xy dy/dt = -y + (x^2) - Determine the critical points for the equation, - Determine the linearized system for each critical point and discuss whether it can be used to approximate the behaviour of the non-linear system. What is the type and...

Homework Statement The following are two first order logic statements of the statement "There are infinitely many prime numbers" 1. http://uploadpie.com/3PZlO 2. [PLAIN][PLAIN]http://uploadpie.com/PN5i8 Can anyone explain why the second one is wrong? Thanks for help! Homework Equations...

Homework Statement Solve x2y'=1-x2+y2-x2y2 The methods I've learned so far are: Separable, Linear, Exact, Homogeneous, and substitution for Bernoulli's D.E. The equation is not linear, exact, or homogeneous. That leaves only two possible methods to use, separate it or get it into the...

Here is an image of the first order linear differential equation and my attempt to solve it. It ends in an integral that can not be solved. http://img831.imageshack.us/img831/9937/math1.gif And here is an image of the first order non-linear differential equation and my attempt to solve...

Homework Statement Well the problem is: translate the following sentences in first order logic. I cannot verify whether they are correct or not. Maybe someone can point out my mistakes. 1. No barber shaves persons shaving themselves. (\neg \exists x)(Barber(x) \wedge (\forall...

This is a concept question i was wondering. in what instances would this be true and in what instances would this be false. im in general chem 2.

Homework Statement Solving the following differential equation with the given boundary conditions: \hbar^2 \frac{d^2}{dx^2}\psi (x) = 2mE\psi (x), \ \ \ \ \ \forall \ \hbar^2,\ m,\ E > 0 \psi(a) = \psi(-a) = 0 Homework Equations The Attempt at a Solution \hbar^2 \frac{d^2}{dx^2}\psi (x)...

Homework Statement In problem 11, determine by inspection at least two solutions of the given initial-value problem. Homework Equations 11. dy/dx = 3y^(2/3) , y(0)=0 The Attempt at a Solution I can't figure out what they mean by inspection, I have no examples to go off from...

Hi, I have the first order differential equation y+y' = x y(0) = 0 First i tried to assume a solution of the form Ax+b, that didn't quite work. Then i tried to use the Integrating factor technique, work follows e^{\int1} = e^x \int e^x(y+y') = \int{xe^x} ye^x = \int xe^x let u = x...

Homework Statement Solve first order ODEHomework Equations \frac{dy}{dx}=x^2+1+\frac{2}{x}y Rearranged \frac{dy}{dx}-\frac{2}{x}y=x^2+1 The Attempt at a Solution Integrating factor p=\exp(-\int \frac{2}{x})=\exp(-2\ln x)=x^{-2} Multiplying through by the integrating factor...

Homework Statement Salt water pours into a 10 liter tank at a rate of 4 l/min. Its concentration is 2 g/l. The brine in the tank is well mixed and it drains out at a rate of 4 l/min. Call y the grams of salt in the tank at time t. The tank is initially full of fresh water. Solve the...

Homework Statement I have a large project involving Runge Kutta numerical solutions of differential equations. I understand the Runge Kutta method and I've done it before, but my problem involves taking the differential equation y''=sin(3y(t)), t>=0 and reexpressing this IVP into coupled...

I have a large project involving Runge Kutta numerical solutions of differential equations. I understand the Runge Kutta method and I've done it before, but my problem involves taking the differential equation y''=sin(3y(t)), t>=0 and reexpressing this IVP into coupled first order...

Homework Statement xy^{'} - 2y = x^{5} Homework Equations e^{\int P(x)dx} The Attempt at a Solution Rearranging the into the form, y^{'} - P(x)y = Q(x) So, y^{'} - \frac{2y}{x} = x^{4} Multiplying both sides by e^{\int P(x)dx} or e^{-2\int \frac{dx}{x}}, Since...

good day everyone. i need to know what test must i make first in dealing with differential equations.. please help me. it's hard for me to figure out whether an equation is homogeneous or exact... there are examples of exact differential equations that have same degrees for M(x,y) and...

Homework Statement y' + Ay2 = B A & B are constants and y is a function of x Find the general solution to the differential equation. (Find y(x)). Homework Equations The Attempt at a Solution This differential equation came up when I was trying to solve a problem in...

First order nonlinear ODE -- Integrating factor + exact differentials, or not? Hello everyone, (I apologize if this did not format properly, if not I will attempt to edit it if that functionality is available upon submitting a question). I recently came across the following nonlinear ODE...

Homework Statement Find the general solution for: x y' - 2y = x +1 (x>0) Homework Equations None The Attempt at a Solution I have literally no idea how to start this. I've tried seperating variables but ended up with: \frac{y'-1}{2y+1} = \frac{1}{x} but that isn't solvable due to the y'-1...

I heard that if you put a laser through a diffraction grating, and then reflect the first order fringes back to the middle point you will create a second diffraction pattern within the bright spot you are creating. I have been asked to try to test this and would like to know whether or not it is...

Let L = {f } be a first-order language containing a unary function symbol f , and no other non-logical symbols. 1.Write down a sentence χ of L which is satisfiable in some structure with an infinite domain but is false in every structure with a finite domain. What can you say about the size of...

1. Homework Statement Let L = {P } be a first-order language with a binary relation symbol P as only non-logical symbol. By exhibiting three suitable L-structures prove (informally) that no two of the following sentences logically implies the other (i) ∀x∀y∀z(P (x, y) → (P (y, z) → P (x...