First order Definition and 546 Threads

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...

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...

Homework Statement Solve (x - \sqrt{xy})dy - ydx = 0 Rearranged gives us -y + (x - \sqrt{xy})y' = 0 And it looks like an exact differential equation, but is it really? Homework Equations For any given exact equation of the form M(x,y) + N(x,y)y' = 0 The following must be true...

Homework Statement Finding the general solution of y'= (2y^2)/e^x and the particular given that y(0) = 0 The Attempt at a Solution I separate variables etc. to get y = -1/(2c-2e^(-x)) where c is the constant. The problem then is obtaining the particular solution. If I substitute y and...

Homework Statement Solve the system of first order differential equations using Laplace Transforms: dx/dt = x - 4y dy/dt = x + y, subject to the initial conditions x(0)=3 and y(0)=-4. Homework Equations So far I've used the limited knowledge of Laplace Transforms for first order...

y'= \frac{y}{1+e^x}+e^{-x} It's an easy first order linear inhomogenous eq. I solved it by hand with the formula that one can find anywhere AND with Mathematica, but when I take the derivative to check the solution it comes out wrong and it's freaking me out. Can anyone here post just the...

I am looking at some of the notes but don't quite understand this. What are the physical explanation of the graphs (Fig 4(a) and 4(b)) on Page 4 ? http://www.pma.caltech.edu/~mcc/Ph127/b/Lecture3.pdf" Why V_{g} decreases with temperature but V_{l} increases with temperature?

Homework Statement Give the physical explanation of the graphs (Fig 4(a) and 4(b)) on Page 4 http://www.pma.caltech.edu/~mcc/Ph127/b/Lecture3.pdf" Homework Equations 1) Why V_{g} decreases with temperature but V_{l} increases with temperature 2) Why must phase transition happen at...

Hi there, how can i solve this first order partial differential equation: grad p= (0,0,-ρg) where p=p(x,y,z,t) is pressure where ρ=ρ(x,y,z,t) is density where grad p is in three dimensional Cartesian coordinates can i just separately solve the three differential equations? ie dpx/dx...

1. rewrite the following equation as two first order ODE's x'' + 2(x^(2) - 2).x' + x = 0 Homework Equations This is what I have so far: x'' + 2(x^(2) - 2) . x' + x = 0 x'' = - 2(x^(2) - 2) . x' - x x' = y y' = -2(x(^2)-2). y - x Are these correct?

I'm trying to solve this equation: Ux + Uy + U = e^-(x+y) with the initial condition that U(x,0)=0 I played around and and quickly found that U = -e^-(x+y) solves the equation, but does not hold for the initial condition. For the initial condition to hold, I think there needs to be some...

I have been asked to write the following two first order equations in matrix form. x' = y y' = -x I also must state that the follow on to the question asks for the only fixed point. The two first order equations came from a modified Van der pol equation.

Could someone explain why the graph of a solution can never cross a critical point?

First order correction to particle-in-box eigenstates for Dirac perturbation Homework Statement Calculate the first three nonzero terms in the expansion of the correction to the ground state \psi^{1}_{1} for a Dirac delta perturbation of strength alpha at a/2 (box from 0 to a). Homework...

Maybe I'm just dumb... y'(t)=y(t)^3+f(t) find y(t) Thanks...

Homework Statement \frac{dy}{dx} = \frac{3xy}{3x^2+7y^2}, y(1)=1 Express it in the form F(x,y)=0 The Attempt at a Solution I'm not sure where I'm going wrong. I let v=y/x, v+x\frac{dv}{dx} = \frac{3x^2v}{3x^2+7x^2v^2}=\frac{x^2(3v)}{x^2(3+7v^2)}= \frac{3v}{3+7v^2} \Rightarrow...

Homework Statement Find the unit step response of the transfer function... a) G(s)\,=\,\frac{4}{s\,+\,4} b) G(s)\,=\,\frac{2}{0.2s\,+\,1} Homework Equations General first order step response equation... C(s)\,=\,R(s)\,G(s)\,=\,\frac{a}{s(s\,+\,a)}, where R(s)\,=\,\frac{1}{s} then do an...

Homework Statement A tank contains 70 kg of salt and 2000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min. Find the amount of salt in the tank after 2 hours. I'm failing to figure out how to manipulate the...

Hi, I tried to solve this by using the integrating factor technique \begin{cases} dy/dt +10y = 1 \\ y(1/10) = 2/10 \end{cases} So p(x) = 10t \rightarrow e^{10t} e^{10t} \cdot \frac{dy}{dt} + e^{10t} \cdot 10y = e^{10t} This part is confusing to me, i have two different variables...

Homework Statement Show that if a and \lambda are positive constants, and b is any real number, then every solution of the equation dx/dt + ax = b*exp(-\lambda*t) has the property that x(t) --> 0 as t --> \infty The Attempt at a Solution i tried considering the cases where a = \lambda and a...

Homework Statement The problem is given as follows: Solve dy/dt + y = 0.5, y(t=0)=1Homework Equations The Attempt at a Solution I separate the y terms from the t terms, which gives me dy(-y+0.5)=dt I integrate both sides to get -ln(-y+0.5)=t+C C is the constant, I combine the constants from...

Homework Statement Solve the differential equation: Homework Equations 1+(x-x^2*e^(2y))(dy/dx) = 0 The Attempt at a Solution No idea how to approach this.

The basic algorithm of degenerate perturbation theory is quite simple: 1.Write the perturbed Hamiltonian as a matrix in the degenerate subspace. 2.Diagonalize it. 3.The eigenstates are the 'correct' states to which the system will go as the perturbation ->0. But what to do if the first...

i have to solve this equation : du/dx * du/dy = x*y u(x,y) = x for y =0 with putting this equation in the form : F(x,y,u,du/dx,du/dy) = 0 . it can be solved. But mine book does not explain how to do this, there are no examples. Can someone help me ? or any links of examples on the...

Homework Statement Find the general solution of the following homogeneous differential equations: (i) \frac{du}{dx} = \frac{4u-2x}{u+x} (ii) \frac{du}{dx} = \frac{xu+u^{2}}{x^{2}} (You may express your solution as a function of u and x together) Homework Equations There are no...

The potential of an electron in the field of a nucleus is: -Ze^2/(4 Pi Epsilon0 r) r > r0 -Ze^2/(4 Pi Epsilon0 r0) r <= r0 where r0 is the fixed radius of the nucleus. What is the pertubation on the normal hydrogenic Hamiltonian? Calculate the change in energy of the 1s state to the first...

Homework Statement \frac{1}{xy} \frac{dy}{dx} = \frac{1}{(x^2 + 3y^2)} Homework Equations used the substitutions: v = \frac{x}{y} ,and \frac{dy}{dx} = v + x \frac{dv}{dx} The Attempt at a Solution took out a factor of xy on the denominator of the term on the right hand...

Homework Statement y' = \sqrt{(1-y^2) } Initial condition y(0) = 0 a) Show y = sinx is a solution of the initial value problem. b) Look for a solution of the initial value problem in the form of a power series about x = 0. Find coefficients up to the term in x^3 in this series...

Consider the following function of space and time for a propagating plane wave were nonlinear effects are included via a constant "B" u(x,t) = u[t - x/[c + Bu(x,t)]] show that u(x,t) satisfies a first order non linear PDE.

Hi I am looking for a firstorder differential eqaution which all of its solution, which there is a point that all of the solution goes thrugh Thank you Ariel

Homework Statement convert y'' +x^2y'+12y=0 to a system of first order equations with initial conditions y(0)=0 y'(0)=7. Homework Equations The Attempt at a Solution first i isolate highest derivative y'' = -x^2y'-12y then i let u_1=y u_2=y' then (u_1)' = u_2 and...

Homework Statement y is a function of t Homework Equations y'+ky(e^-t)=l(e^-3t) The Attempt at a Solution Considering that the equation is of the form dy/dt + p(t)y =q(t) , I have been looking for an integrating factor of the form: e^{integral[p(t)dt]}, where p(t) = ke^(-t) If I...

Homework Statement Find two non-zero terms of the power series solution of y' = 1 + y^2 ,y(0) = 0 by using series substitution y(x) = sum (k=0 to inf) [a][/k] *x^k Homework Equations The Attempt at a Solution First take the derivative of the power series to get y' =...