First order Definition and 546 Threads

With the help of harmonic gauge condition, graviton propagator can be obtained by weak field expansion around the flat Minkowski metric (assuming cosmological constant is zero). Gravitation theory can also be written in the first order (Palatini) formalism. In stead of the metric, the basic...

Solve: dx / dt = 3*x + y dy / dt = -y As for solving this, here is what I've got so far: Since dy/dt is separable, I found that dy / y = -dt, integrated, and solved explicitly for y: y = Ce^-t I then plugged Ce^-t for y in the dx / dt portion of the system and found that...

Hello everyone I'm stuck with a problem from Simmons (not HW). The problem asks to solve the following equation by finding an integrating factor (xy-1)dx + (x^2 - xy)dy = 0 I found by hit and trial that there can be no integrating factor that is a function of x alone or y alone. So how...

Hi. Do you know any sources where I can find good problems about first order differential equations? Thanks...

I have the following equation: (x^2-y^2-y)dx-(x^2-y^2-x)dy=0 I was trying to find the integral factor of this to make it a exact differential equation, but ended in a almost imposible integral. do anyone have any idea of how to make this?

I'm having serious trouble understanding how to solve this problem using the differential equation method ( I MUST use this method). I provided the answer but my solution attempts are not producing the same result. Here is the problem...

Please click the image to make it larger: http://img360.imageshack.us/img360/2049/82009866sy5.th.jpg To solve this circuit I'm going to use the differential equation approach. I'm concerned with the voltage across the capacitor at V_c(0^-) and V_c(0^+) At position 1 before the switch...

[SIZE="4"]We are doing transient circuit analysis in one of my engineering courses. There are two ways of solving these types of circuits: 1. The step by step approach 2. The differential equation approach. The step by step method is well documented in our textbook, but the differential...

I have run into this problem solving differential equations of this type (they occur often doing momentum problems): kxy = (y+dx)(x+dy) where k is constant. I multiply it out to : kxy= xy + xdx + ydy + dydx Regroup and : [tex] \int {kxy} = \int {xdx} + \int {ydy} + \int {dydx} [/itex]...

Homework Statement Solve the following differential equation using separation of variables (1+x)^2 y' = (1-y)^2 , y(1) = 2 Homework Equations The Attempt at a Solution haven't gotten very far in this at all :/ i've tried dividing both sides by (1+x)^2, in order to get y' on it's own...

Homework Statement Given the below stated equations I need to find the exact polynomial given the initial condition. y(0) = 1 y = 4*t*sqrt(y) Homework EquationsThe Attempt at a Solution I simply disregard the initial value condition and get y = t^4 How can I find the fourth order...

I've been kind of self teaching myself first order derivities... this is really my first shot at it.. want to know if this is right so far \frac{dy}{dx} = \frac{y(1-x^5y)}{x} xdx = y (1-x^5y)dx xdy = (1y-x^5y^2)dx xdy = ydx - x^5y^2dx \frac {xdy - ydx}{y^2} = \wr -x^5dx \wr d\frac{x}{y} =...

"Find the general solution to the differential equation by separating variables: 3tany - dy/dx(secx) = 0" This is what I set up: 3tany dx = secx dy 1/secx dx = 1/3tany dy cosx dx = 1/3tany dy [int] cosx dx = [int] 1/3tany dy sinx = (1/3)ln|sinx| I'm stuck as to what to do next...

I'm having trouble solving first order differential equations for euler's method. right now I'm trying to figure out: y' = x + y y(0) = 1 i have: dy/dx - y = x p(x)=-1 , q(x)=x u=e^(-x) y=e^x [integral](xe^-x)dx .. i don't think I'm doing this right, where am i going...

u_x+u_y+u=e^{x+2y}, y(x,0)=0 I have no idea how to do this. We were only taught how to solve homogeneous first order PDE's.

The first-order differential equation y' +(ex^2+1+1/x^2)y=0, with boudary value y(1) =1 Using, asymptotic mathcing to study the behaviour of the sltion as e tends to +0, when x is not too large, the term ex^2 is negligible so an approximate equation for y is y'_L +(1+1/x^2)y_L=0 . When...

The first-order differential equation y' +(ex^2+1+1/x^2)y=0, with boudary value y(1) =1 Using, asymptotic mathcing to study the behaviour of the sltion as e tends to +0, when x is not too large, the term ex^2 is negligible so an approximate equation for y is y'_L +(1+1/x^2)y_L=0 . When...

Hello all, I'm trying to prove to myself that the following solution to the DE shown works. I can't start using it until i prove to my self it works (it's this psycological thing i have were i can't use anything unless i know where it comes from). :smile: Here is the Equation and it's...

I am new to to this topic, hints? y^1=x+5y The only examples are in the form dy/dx+p[x(y)]=Q[x]

Can anybody tell me what can be the solution of this differential equation? (dr/dt)^2=a/r^2+b/r+c Is first order and i need some ideas about solving it

Hi! I'm new here, but I hope that someone would evenly help me! My first question is about the problem (3.3 on page 100 from Loudon - The Quantum Theory of Light 3ed) in the attachment; the second question is about discussing (I)the physical origin of fluctuations of the electromagnetic...

I would like to solve a problem of the type (da/dt)^2 + f(a)* (da/dt) = g(a) (1) a=a(t) unknown function f(a), g(a) = known functions of a. This differential equation is a first order ODE but (da/dt)^2 makes it different compared to a typical first order ODEs (at least to my...

Hello. I am taking a self study diff e course, and I have run into a problem with no one to ask for help. Here is the problem: y\prime=1+x+y^2+xy^2 The question asks to find the general solution. I simply don't understand how to solve this problem. Here is the direction I am going in...

Does anyone see how one can tackle the following ODE? [2y*exp^{y/x} + x}] \frac {dy} {dx} -2x - 2y = 0 that is my attempt: rearrange to get dy/dx = \frac {2x + 2y} {2y*exp^{y/x}-x} I do not see how to go on from here. Surely, the ODE is not seperabale and I don't find a way...

i've derived the following differential eqn from a problem I'm working on, and i have tried in vain to solve this if anyone can give a direction where i should go our how to attack would be greatly appreciated. the eqn is I\,r= -L\dot{I}+\frac{3}{2}\mu_{0}m R^{2}\frac{z...

Hello everyone. I'm going back to all my old webworks and trying to finish them and I'm still having problems on first order. It says this is seperable but I'm not seeing it. Here are the directions: The differential equation...

We have the first order ODE y'=4t \sqrt y,~y(0)=1, for which i have found the exact solution, namely a fourth order polynomial. I want a numerical method to solve the problem exactly. This method has to be a fourth order method, since this implies that the local error vanishes. Now...

Just need a hand with this one. (dy/dx)x + 2y = x^3.ln(x) (dy/dx) = (x^3.ln(x) - 2y)/x Integrating factor = x^2 (dy/dx)x^2 + 2xy = (x^3.ln(x))x^2 yx^2 = INT[(x^3.ln(x))x^2] I'm having trouble integrating the last part to complete it. Thanks a lot and in advance for any help.

Hi, As far as I know this is a first order, nonlinear diff eqn with both dependant and independant variables...so it is not solvable?? y'+ay^2 = bx If anybody knows if there is a method to solving it, please let me know. Thanks, danmag :confused:

The first-order reaction, SO2Cl2 --> SO2 + Cl2, has a rate constant equal to 2.20 x 10-5 s-1 at 593 K. What percentage of the initial amount SO2Cl2 will remain after 2.00 hours? a.1.00% b.14.7% c.17.1% d.85.4% ln [a]t/[a]0 = -kt ln [a] = -(2.20 x 10-5...

I'm using an integrating factor, rho(x), to solve an equation of the form dy/dx + P(x)y = Q(x) I need to find the particular solution. y' = 1 + x + y + xy; y(0) = 0 y' - y - xy = 1 + x dy/dx + y(-1-x) = 1 + x P(x) = (-1-x), Q(x) = (1 + x), rho(x) = e^(-x-1/2x^2) (Multiply both sides by rho(x))...

So I'm a bit confused about these metatheorems about first order logic, partly because I haven't read any of the real proofs, but I just want to know the results for right now. Here is what I understand: Soundness means that any derivation from the axioms and inference rules is still valid...

I have the following problem that i can't get the right answer to: y'+y=5sin(2t) I find the integrating factor u(t)=e^t multiply the whole function u(t) and i get (ye^t)'=5e^tsin(2t) I do integraton by parts on the second part and get 1/9 for the coefficents, in the calculator they...

YATP - Yet Another Trainlike Problem Sailboats A and B each have mass 60kg and cross the starting line at the same time of a race. Each has an initial velocity of 2m/s. Obviously from this, m1 = m2 == 60kg and vo1 = v02 == 2 m/s. The wind applies a constant force of 650N to each boat and...

I need to solve the following for f(s): (s^2 + 1)f '(s) + s f(s) = 0 First I isolated for f '(s), which gave me: f '(s) = -s f(s)/(s^2 + 1) Then, d f(s)/ds = -s f(s)/(s^2 + 1) so, d f(s) = (-s f(s)/(s^2 + 1))ds Integrating I get: f(s) = -F(s)ln(s^2 + 1)/2 + C, where F(s)...

Hello I'm struggling with this concept, can't seem to get my head round it or find any good reference sites or books. I have calculated the eigen values and eigen vectors for the following matrix 5 3 1 7 Eigen values 4, 8 Eigen vectors 4: 3 -1 Eigen...

How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.

How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.How i can solve a system of 6 first order differential equations by using numerical techniques like Euler method, RK-4th order method , ODE -45 etc.

I thought the general solution of the linear first order differential equation y ^{\prime} + p(t)y = g(t), \qquad y\left( t_0 \right) = y_0 were y = \frac{1}{\mu (t)} \left[ \int \mu (s) g(s) \: ds + \mathrm{C} \right], where \mu (t) = \exp \int p(s) \: ds However, I have found...

"A recent college graduate borrows $100,000 at an interest rate of 9% to purchase a condominium. Anticipating steady salary increases, the buyer expects to make payments at a monthly rate of 800(1 + t/120), where t is the number of months since the loan was made. Assuming that this payment...

Just need some verification. Question 1 Find the general solutions of the following first order PDE z_x - yz_y = z Question 2 Find the general solution of the following first order PDE x^2z_x+y^2z_y = xy

Solve y’ – y*tan[x] = 2sin[x]. I keep arriving at the answer: y = 2ln(sec[x]) / sec[x] - c/sec[x] for this question. According to my textbook the correct answer is: y = (c - cos[x]) * sec[x]. Can anyone explain how to obtain this answer? Thanks :)

To do a tableau proof of this statement: (\forall x) [P(x) \vee Q(x)] \supset [(\exists x)(P(x) \vee (\exists x)(Q(x)] I started out by restating it as follows: (\forall x) [P(x) \vee Q(x)] \supset [(\exists y)(P(y) \vee (\exists z)(Q(z)] to avoid confusion over what's bound to what (and...

I am looking for a method to solve coupled first order PDEs in following form: \frac {\partial u1} {\partial x} = f(x,t,u1,u2) \frac {\partial u2} {\partial t} = g(x,t,u1,u2) Subject to prober BC and IC. and consider: u1=F(x,t) u2=G(x,t) I am looking for...

Hello, It has been over a year since I last did calculus. And I am having trouble with my current calculus course. First here is the question: Solve the given first-order linear equation and verify that your solution indeed satisfies the equation. y' - 2xy = 2xe^x^2 Now I THINK I...

Is total formalization possible? If not, why not? The following is a first course in formal mathematical logic. http://www.trentu.ca/academic/math/sb/pcml/pcml-i-15.pdf Looking through the book, I do not see any that the author presupposes any mathematical knowledge. Volume II...