First order Definition and 585 Threads

Can anyone help me to solve a differential equation? I want to solve ∂v(p,t)/∂t=-p^2 v(p,t)-sqrt(2/pi)∫v(p,t)[1-δ(t)R(t)]dp+sqrt(2/pi)[δ(t)R^2(t) C] with initial data v(p,0)=0 where C is constant and the integration from zero to infinty Any suggestion please? Solution by volterra integral...

Hi. When using approximations such as g = n + h where h is much less than n ; what does " valid to first order in h" mean ? Does it mean include terms linear in h or does it mean drop those terms ? Thanks

Homework Statement ##y' = \frac{cos x}{sin y}## ##y' = \frac{6x^2}{y(1 + x^3)}## Homework EquationsThe Attempt at a Solution So I was working through some textbook problems and there's something about the solutions of the above equations I don't quite understand. The first one: ##\int sin...

Homework Statement What is the general solution of: y'=(3*y^2-x^2)/(2*x-y) Homework EquationsThe Attempt at a Solution This First Order equation is neither linear nor separable. I also have checked the Exact test, which turns to be Not Exact. Any help regarding how...

Homework Statement Solve dy/dx = y/x + tan(y/x) Homework EquationsThe Attempt at a Solution Not separable, as far as I can tell. It's not homogeneous, since for the tan term f(λx,λy) = tan(λy/λx) = tan(y/x) ≠ λtan(y/x). It's also not of the form dy/dx + P(x)y = Q(x), because I don't think Q(x)...

http://arxiv.org/abs/1503.08640 New first order Lagrangian for General Relativity Yannick Herfray, Kirill Krasnov (Submitted on 30 Mar 2015) We describe a new BF-type first-order in derivatives Lagrangian for General Relativity. The Lagrangian depends on a connection field as well as a...

Homework Statement dv/dt = 9.8 - 0.196v Set in correct form: dv/dt + 0.196v = 9.8 Since p(t) = 0.196, u(t) the integration factor is given by: u(t) = e∫0.196 dt Multiply each term by u(t) and rearrange: (e∫0.196 dt)(dv/dt) + (0.196)(e∫0.196 dt)(v) = (9.8)(e∫0.196 dt) From now on we will set...

Question: ##h_{t}+vh_{x}+v_{x}h=0## ##v_{t}+gh_{x}+vv_{x}=0## Write it in the form ##P_{t}+Q_{x}=0##, where ##P=(h,hv)^{T}##, where ##g## is a constant ##>0##, and ##v## and ##h## are functions of ##x## and ##t##. Attempt: I have ##Q=(vh,?)^{T}##, the first equation looks easy enough, but...

I don't understand this first order differential equation: https://lh5.googleusercontent.com/UUpQF4YjmjJRPvFuzGg2MhpMMMDyi2KFZPCKMKVIXGREc1owvXDzGR0bcA=s600 How is it possible to get an exponent as answer?

Homework Statement Homework Equations [/B] Tao = R(th) C The Attempt at a Solution The unknown DC circuit model consists of a V(th) and R(th) Tao = (R(th) + 3000) C , total resistance of circuit is R(th) + 3000 0.004 = (R(th) + 3000) (1x10^-6) R(th) = 1 kOhm The V(th) should oppose the...

I'm searching for a reflexive diffraction grating with at least 1500 line per mm and high intensity in first order. Common reflexive diffraction grating don't have enough intensity for my experiment. I need to help for getting such grating. Thanks

Homework Statement Use the substitution ##x=X+h## and ##y=Y+k## to transform the equation ##\frac{dy}{dx}=\frac{2x+y-3}{x-2y+1}## to the homogenous equation ##\frac{dY}{dX}=\frac{2X+Y}{X-2Y}## Find h and k and then solve the given equation Homework EquationsThe Attempt at a Solution If I...

Homework Statement We are given K1 = 0. So the answer should be in the form of V(x) = K2e^(-t/z)Homework Equations V=IR V(x) = K1 + K2e^(-t/z) V(infinity) = K1 V(0+) = K1 + K2 z = RC The Attempt at a Solution I draw the circuit for t = 0- and find the voltage across the capacitor. Vc(0-)...

(1) Anyone who is thin, tall and energetic will be good basketball player. (2) Some people are tall but not good basketball players. (3) Anyone who do exercise or eating healthy food will be energetic. (4) Saman is thin and tall person who do exercises. Write the above sentences in First Order...

Hello PF! We were doing mass balances on mixing tanks in one of my ChemE courses, and in one of the problems we arrived at the following DE: \frac{dC_B}{d \theta} + 0.025C_B=0.0125 e^{-0.025 \theta} Where CB is the concetration of salt in the tank and θ is time. The professor made us solve the...

Homework Statement The Attempt at a Solution The first part is fairly simple I think. It's just rate of accumulation = rate of generation - rate of output(losses) I'm not too sure how to solve this differential equation. I divide the whole equation through by mc and rearrange but I keep...

Homework Statement $$y' y + \frac{y}{x} = 1 - 2x$$ Homework Equations nothing comes to mind The Attempt at a Solution i've guessed a quadratic but that didn't work. now I'm stuck. any ideas? also, this is not homework, but a problem I am working on. Thanks!

Hi, can anybody help me with this differential equation? (px-y)(py-x)=a^2*p, where p=y'. I tried to solve it by expliciting the two solutions for y as functions of p and x and then derive, in order to obtain two first order differential equations in p but these are impossible to solve. I also...

1. The problem statement, all variables and given/known da ##\frac{x^{2}}{k^{2}} + \frac{y^{2}}{\frac{k^{4}}{4}} = 1## with k != 0 this can be simplified to ##x^{2} + 4y^{2} = k^{2}## Find dy/dx implicitly, then find the new dy/dx if you want orthogonal trajectories to the ellipse. Lastly solve...

Hello, I have the following PDE : v_y \frac{\partial f}{\partial y} + \Omega_x(y)\left(v_z\frac{\partial f}{\partial v_y} - v_y\frac{\partial f}{\partial v_z}\right) + \Omega_z(y)\left(v_y\frac{\partial f}{\partial v_x} - v_x\frac{\partial f}{\partial v_y}\right) = 0 (which is the steady...

How to find L if the form is: $$ (\frac{\partial L}{\partial x})^2 - (\frac{\partial L}{\partial y})^2 = -1$$ The author wrote, $$L = y + ax^2 + ..$$ but I didn't get how?

Homework Statement Solve the given the two equations: xdy + ydx = ydy and (y^2 + 1)dx +(2xy + 1)dy = 0 Homework Equations N/A. The Attempt at a Solution For the first, I can see that solving this with respect to dy/dxmight be a bit tricky. However, if I solve it for dx/dy, things...

Homework Statement Solve the following IVP: ##\frac{\partial v(x,t)}{\partial x} + \frac{\partial v(x,t)}{\partial t} + v(x,t) = g(x,t)## Homework Equations The initial values: v(0,t) = a(t) and v(x,0) = b(x)The Attempt at a Solution I applied the Laplace transform x -> s to get...

In first order correction of wavefunction, |ψ(1)n>=∑ψ(0)m<ψ(0)m|V|ψ(0)n>/(E(0)n−E(0)m) when any two of the original states degenerate, we replace the two states with their corresponding "good states" to get a new set of "undisturbed" states (ψ(0)m), AND then we determine the first order...

In the same way one can show that \nabla^{2}\theta=0 has only one smooth solution, namely \theta=0, I would like to show that \gamma^{i}\partial_{i}\epsilon=0 has only one smooth solution, where \gamma^{i} is a Dirac gamma matrix (or an element of the Clifford algebra), and \epsilon is a...

Homework Statement 8t^2 * y'' + (y')^3 = 8ty' , t > 0 Homework EquationsThe Attempt at a Solution I tried using the substitution v = y' to get: 8t^2 * v' + v^3 = 8tv I rewrote it in the form 8t^2 * dv/dt + v^3 = 8tv, and then moved the v^3 to the other side to get 8t^2 * dv/dt = 8tv - v^3...

So I saw this a moment ago: How can the second and third terms yield (n+1)+(n-1)=2n and not (n+1)+n=2n+1? PS: I solved the problem by using [a,a(+)]=1. Sorry, this is very simple but I cannot figure out what I did wrong.

Homework Statement If y=y(t) is the solution of the initial value problem { y'+(2t+1)y=2cos(t) y(0)=2 then y''(0)=? it is a multiple choice practice problem with choices y''(0)=2 y''(0)=-2 y''(0)=4 y''(0)=0 y''(0)=-4Homework EquationsThe Attempt at a Solution Im really not sure how to go...

Homework Statement If y = y(t) is the solution of the initial value problem y' + (2 t + 1) y = 2 cos(t) y(0) = 2 What is y''(0)? Homework EquationsThe Attempt at a Solution Since this is a first order linear, I started out by finding the integrating factor so I can find what y is, and then...

How do I go about solving a differential equation of the form \partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y) Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients...

Hi, I need help solving this ode, when I try to solve it I end up with a big crazy answer and I believe it should be simpler. (dy/dx)^2=((ay^4)/2)-(a+1)y^2+1 y(0)=0, y'(0)=1 and a is within [0,1]

I'm going to need a little help with this one. I get an answer but it doesn't make sense. The question states According to Newton's law of cooling, the time rate of change of temperature T(t) of a body immersed in a medium of constant temperature A is proportional to the difference A-T. That...

(r^2) (dT/dr)+B*r*T=T^2, with initial condition dT/dr |r=0 =0 where B is a constant I've gotten it to this: dT/dr = -BT/r + T2 / r2 by dividing everything by r2, then I substitute using λ= T/r which gives: r * dλ/dr + lambda = -B * (λ) + λ^2 I don't know how to separate...

Hi :-) I'm currently learning about wave interference and came across two phrases I can't seem to find the meaning of; first order minimum and second order minimum. What do they mean an how are they used? I presume they are for the order of destructive interference or something?

Hi How do you calculate the following indefinite integral: \int \frac{2x}{125+3t} dt a step by step solution would be appreciated

I was wondering if there is a way to get specific numerical values for the following differential equation: f'(x)+ \frac{1}{x-20}\cdot f(x)=\frac{1}{x-20}\cdot g(x) I have numerical values for g(x) for about 10 different x values. I need to find f(x) numerically for those same values...

Homework Statement okey, so i got stuck at another step in the way of solving de's.I've been studying DE of this form: y' + P(x)y = Q(x) Homework Equations The Attempt at a Solution So, first we solve y' + P(x)y=0 for y. \frac{dy}{y} = -P(x)dx , we integrate this and get...

Homework Statement I'm starting college this autumn(physics) and I started learning some calculus on my own, basic stuff like first order differential equation and so on.Recently i stumbled on something that i don t understand.I was reading the course and re-solving the given examples for...

For this problem, I am stuck on the actual system. I don't see what substitution I can make, and the fact that ##u(v)## is a piece-wise function is tripping me up. How the heck do I approach this?? This doesn't look like a standard problem at all.

If: ##\hat{H} \psi (x) = E \psi (x)## where E is the eigenvalue of the *disturbed* eigenfunction ##\psi (x)## and ##E_n## are the eigenvalues of the *undisturbed* Hamiltonian ##\hat{H_0}## and the *disturbed* Hamiltonian is of the form: ##\hat{H} = \hat{H_0} +{\epsilon} \hat{V}...

For a regular LR circuit (L and R in series) and with a AC voltage: I tried to derive the solution myself. https://www.dropbox.com/s/jmsu9j0vt91ze8x/LRcircuit.jpg So first I solved with undetermined coefficients, plugged them in, and then solved with Cramer's Rule. Then I added...

I know how to do a Linear First Order and I know how to do a Bernoulli (kind of). The kind of part may be why I'm having a problem. dy/dx+xy=xy^2 So I know in order for that to be a normal linear differential, that square on the last y has to go away somehow... I'm not sure how to do this...

the question is to find I(0)- and I(0)+ the I is at the what I have attempted finding Req on the right side I eliminate the capacitor and Req = 12*6/(12+6) = 4 so Vc (0)- = Req/(Req+12) *18 = 9/2 T = Req*c= 4*1/12 = 1/3 so V(t) = 18/4 e^(-3T) so I (0)- = V(t)/12 = 3/8 e^(-3t)...

How did they get the blue box? I know where they got the 0.5 inside the brackets from but not sure about the rest. The bode plot in my data book has log10(wt) as the x-axis..

Homework Statement a) Starting from the statement that total entropy (Ssystem+Ssurr) can only increase, show that G = U - TS +pV will attain its minimum value for a system in equilibrium with a fixed pressure and temperature reservoir. b)At atmospheric pressure, a particular substance is...

I think I mostly understand how this works, and it makes intuitive sense. However, I'm a little bit confused by one step in the proving of this. On the second page of the attached PDF, there is this statement: x' + kx = (r/k + c2)δ(t) ... (followed by the cases of t<0 and t>0 What comes...

Homework Statement Hi I got this problem and have to fill out this table. Homework Equations node analysis time constant = RC ic(t)= C dVc(t)/dt The Attempt at a Solution I got few answers which i worked it out. i (0-) = 0 Vc(0-) = 1.84 Vr(0-) = i (0-) *...

I've been looking into diffraction for AOLM and stuff like that, and these produce diffraction. Binary Spatial Light Modulators like Digital Micromirror Devices also produce diffraction. This diffraction is then focused and filtered using a pinhole. But, and here is the question: Why is always...

Homework Statement a function has the feature that at any point, the product of its gradient and the x-cordinate is equal to the square root of the y-cordinate multiplied by 5. Part A: Write out a differential equation that describes the function Part B: If the curve passes through the point...

Here is the question: I have posted a link there to this thread so the OP can view my work.