First order Definition and 546 Threads

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} =...

Hello: I discovered this forum while looking for advice on solving a first order nonlinear differential equation. The equation I am trying to solve is dy/dx=(3ay+3bx^2y^2)/(3x-bx^3y) a and b are constants. The equation is not exact, nor is it homogeneous. I have failed to separate the...

Homework Statement For the d.e y' = x^2+y^2 Show that the solution with y(0)=0 has a vertical asymptote at some point x_0, Then I have to try and find the upper and lower bounds for x_0 I'm not able to solve this for y because when I bring the y^2 to the LHS The Attempt at a...

EDIT: Sorry... I have to use perturbation theory. My mistake. Hey... I have a quick question. I have to calculate the approximate change in energy via variation theory when the 'error' Hamiltonian for the Stark effect is defined as: |\vec{E}|cos\theta\bullet eR If I'm not mistaken, the change...

Ok, let's say I have a first order circuit with i_s = Acos(wt+phase) (like in the pic). I'm having problem with the private solution, let's say I pick my private solution like this: i_p = Bcos(wt + phase) = Ccos(wt) + Dsin(wt) (right?) After I place this i_p in the equation I come up with...

-d[A]/dt = k[A] - Int( d[A]/[A]) = Int (k dt) - ( ln[A] + ln[A0] ) = kt ln[A] = -kt - ln[A0] Where am I wrong?

dear friends, i need to solve analitically(also by means of approximate methods) the following nonlinear differential equation: (A+BTs^(3))*dTs/dt+C*Ts^(4)=D where Ts is a function of t. A, B, C and D are costants. the initial condition is Ts(0)=Ti. I would be so grateful if anyone can...

(dq/dt) + (5/(20+t))q = 20/(20+t) ... t=0 , q=1 (a) Find the charge on the capacitor at any time. This is linear so i found the integrating factor which is (20+t)^5 and solved q(20+t)^5 = 20 integral ((20+t)^4) dt and got q(20+t)^5 = 4((20+t)^5) + C my C value i got was...

I have a problem solving a first order differential equation: dT/dP - C2/T = C1 Where C2 and C1 are just constants, the differential equations book I have does not address the situation of 1/T. I am trying to develop my own integrating factor but it would be nice for a little guidance.

Hello, I have been struggling at solving what I think is a system of 1st order PDEs. Here is what I have: \frac{dy1}{dt1} = y1*F1(t1,t2) + F2(t1,t2) \frac{dy2}{dt2} = y2*F1(t2,t1) + F2(t2,t1) These equations have been obtained after modeling a problem using the game theory. More...

Homework Statement u'''-8u''+2u'-3u=0 Homework Equations The Attempt at a Solution So I let: x1 = u then x1' = u' x2 = u' then x1' = x2 and x2' = u'' x3 = u'' then x2' = x3 and x3' = u''' I have only done these problems with second order equations, so I don't understand...

Let be the first order ODE's y'(x)g(x)=0 and y'(x)g(x)=\delta (x-a) except when x=a the two equations are equal , however the solutions are very different y(x)=C and y(x)= C+ \int dx \frac{\delta (x-a)}{g(x)} or using the properties of Dirac delta y(x)=C+\frac{1}{g(a)}...

Hi , Can anybody help me to solve this question? A time varying Hamiltonian H(t) induces transitions from state |k> at time t=0 to a state |j> at time t=t' with probability P(k to j(t')). Use first order time-dependent peturbation theory to show that if P(j to k(t')) is the prababilty that...

hello, while working on a problem i encountered the following integral :(limits are zero and infinity) Integral[J1(kR)dk] J1 is the first order bessel function..cudnt put 1 in subscripts.. Is there an analytical solution for this?? also is it possible to integrate it numerically...

Homework Statement dy/dt = ty(4-y)/3 y(0) = y_o Suppose y_o = 0.5. Find the time T at which the solution first reaches the value 3.98 Homework Equations I separated, integrated and solved, so do i just plug in y_o wherever i see y and 0 for t to find the constant C and plug this...

Homework Statement \frac{dy}{dx} = \frac{x^2}{2} + \frac{xy}{2} + \frac{3y^2}{2} + \frac{3y}{2} Homework Equations The Attempt at a Solution Don't really know were to begin. If anyone could tell me which method to use that would be great. I can't think of any way to solve this.

So this equation came up: xy' + y = cos x Now I was just wondering how to solve this, all I've learned how to do is separation of variables, which cannot be used in this case. Basically I ask this because a solution for y is an infinite series, so basically I'm just wondering if the...

Homework Statement I have two questions: 1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1) 2)I have two second order ODES X''=... and Z''=... to solve this, we make the...

Homework Statement I have two questions: 1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1) 2)I have two second order ODES X''=... and Z''=... to solve this, we make the...

[SOLVED] Seperation of variables - first order PDE Homework Statement I have the expression X'(x)/X(x) = cx. How do I separate the variables? It's the fraction on the left side that annoys me. I know that X'(x) = d(X(x))/dx, but I can't use this here? EDIT: Sorry for the mis-spelled title...

If I have P l- Q in FOL and P is closed, can I infer l- P -> Q. IIRC, this is valid as long as P is closed, but my memory is a little hazy. Is that how it works?

I am having trouble solving the following nonlinear first order differential equation: dy/dx = mx + b - k*y^2 The variables m, b and k are constants. I have had DE in school, but it was mostly linear first order, so I am not sure how to solve this one. Someone has recommended...

Hello everybody, I have a problem here related to QFT in a research project. I end up with some Dirac equation with space-time dependent mass in 2 spatial dimensions. More mathematically, the PDE to solve is \left( {i\left( {\sigma ^i \otimes I_2 } \right)\partial _i + g_y \varphi...

Help with first order, "Bernoulli" ODE We just covered: -First order linear ordinary differential equations -Bernoulli Equations -Simple substitutions. This problem was assigned. Its supposedly a Bernoulli equation with respect to y, but I can't figure it out...

Homework Statement \frac{dy}{dx} + x^{2} = x Homework Equations Above. The Attempt at a SolutionAfter rearranging, I am stuck at \int \frac{1}{x-x^{2}} dx = \int dt I can't think of any u-substitution, or any other trick for integrals I could use to solve this.

Homework Statement In a particular cosmological model, the Friedmann equation takes the form L^2 (a')2 = a^2 − 2a^2 + 1, where L is a positive constant, the dot denotes time differentiation, and the initial condition is a(0) = 1. What are the units of L? Show, without solving this...

Homework Statement This problem is from Blanchard "Differential Equations" Chapter one review, question 32. {\frac {d}{dt}}y \left( t \right) -{\frac {y \left( t \right) {t}^{3}} {1+{t}^{4}}}=2 The Attempt at a Solution Using an integrating factor yields: {\frac {d}{dt}}...

Homework Statement Solve the following differential equation: y' = (y/x) + (2x^3Cos(x^2)/y). Homework Equations The Attempt at a Solution You certainly can't separate variables here and you can't put it in the form in which you can find the integrating factor. This is not a...

[SOLVED] Mixing Problem - Linear First Order ODE Homework Statement A 500-gallon tank initially contains 50 gallons of brine solution in which 28 pounds of salt have been dissolved. Beginning at time zero, brine containing 2 pounds of salt per gallon is added at the rate of 3 gallons per...

1) Solve y' + (1/t) y = t^3. Integrating factor =exp ∫(1/t)dt =exp (ln|t| + k) =exp (ln|t|) (take constant of integration k=0) =|t| ... and then I've found that the gerenal solution is: y = 1/|t| + [c + ∫(from 0 to t) |s| s^3 ds] Is this the correct final answer and is there any way...

hi, could someone explain to me why the sentence - There are exactly two purple mushrooms is represented in FOL like this: (Ex)(Ey) mushroom(x) ^ purple(x) ^ mushroom(y) ^ purple(y) ^ ~(x=y) ^ (Az) (mushroom(z) ^ purple(z)) => ((x=z) v (y=z)) especially the last part i have problem with...

Hello everyone, I am dealing with the following problem. Solving and kinetic equation I came up with the expression H_1^(-1)[H_0(P(r))/q] where H_0 is the zero order Hankel transform, H_1^(-1) is the first order inverse Hankel transform P(r) is a function that depends on the radial...

Can some explain me why first order term in perturbation expansion of scattering matrix gives no contribution for every possible IN and OUT states? It is said that this is connected with the fact that condition of energy-momentum conservation cannot be satisfied for real photons and electrons...

Homework Statement Find the general solution of 2y(x^3+1)dy + 3x^2(1-y^2)dx = 0 Homework Equations The Attempt at a Solution So I first grouped the terms with dy or dx 2y/(1-y^2) dy = -3x^2/(x^3 +1) dx after integrating both sides and solving, I got ln (1-y^2)=...

Im going over some class notes on LTI systems, and attempted a problem involving first order systems. I have attached the problem, it is on page 1B.2 of the attached pdf (its in italics) Also, I have attached a word doc showing my hand working many thanks in advance

Homework Statement Find all solutions x^{2} y y\prime = (y^{2} - 1)^{\frac{3}{2}} Homework Equations The Attempt at a Solution I know I have to use separation of variables because it isn't linear. so I get \frac{ydy}{(y^{2} - 1)^{\frac{3}{2}}} = \frac{1}{dxx^{2}}...

Homework Statement Find the General Solution: xy\prime + (\ln{x})y = 0 Homework Equations The Attempt at a Solution so I used the separation of variable method to get \frac{y\prime}{y} = -\frac{\ln{x}}{x} Then I took the integral of both side to get \ln{y} =...