First order Definition and 585 Threads

In linear algebra, you can have systems of differential equations represented by matrices. What does a "trajectory graph" of such a system show, exactly? And how can you draw one? What's the difference between such a trajectory-graph and an ordinary slope-field for a single linear...

Homework Statement dy/dt=y(9-y) y(0)=2 Homework Equations The Attempt at a Solution dy/(y(9-y)) = dt ∫dy/(y(9-y)) = ∫dt partial fraction decomposition 1=A/y + B/(9-y) 1=9A-Ay +By 1/9=A 0=1/9 +B B=-1/9 1/9∫1/y -1/9∫1/(9-y)=t+C 1/9ln|y| -1/9(ln|9-y|)...

Here is the question: Here is a link to the question: General solution of dy/dt=k((y)(b-y))? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

cosx(dy/dx) + ysinx = sinx cosx (dy/dx) + y/cosx = 1 e^integral (1/cosx) ? I feel like this has to do with ln again but not sure

4y'=e^(x/4) + y First I need to divide through by 4 correct? To obtain y'=(e^(x/4))/4 + (y/4) But then when I try to find integrating factor I just come up with e^(x/4) which I think is incorrect

Re: Logan's question at Yahoo! Answers involving an IVP with a linear 1st order ODE How would I solve a DE like t(dy/dt) + 7y = t^3 dy/dt +7y/t = t^2 Then do I need to find the integrating factor?

Homework Statement Suppose we put a delta function bump in the center of the infinite square well: H' = \alpha \delta(x -a/2), where \alpha is constant. a) Find the first order correction to the allowed energies. b) Find the first three non-zero terms in the expansion of the correction...

Homework Statement I am familiar with the standard method of obtaining a solution to a first-order, linear D.E. (i.e. using an integrating factor). However, consider the D.E. if'(x) = qf(x). It seems (after recasting the equation in the proper form) the solution suggested by the above...

Homework Statement dy/dx = 3 - 6x + y - 2xy Homework Equations dy/dx + p(x)y = c p(y) dy = q(x) dx The Attempt at a Solution Just realized where my mistake was, sorry!

With the statement of: "The circuit is at steady state before the switch closes" Does this means when t<0, the inductor is at steady state and it is short circuit. Am I correct? Then when t>0, the switch is closed and the inductor is also in a steady state? When t=∞, the inductor is...

Hi, I'm having trouble understanding what to do when a First order equation has an inequality at the end of it. For example : sqrt(y-x^2y)*dy/dx = -xy where -1<x<1 I've solved the differential equation with y = 1/4(2C*sqrt(1-x^2) + C^2 -x^2 +1) where C is a constant. What do I do with...

Homework Statement (8x^2y^3-2y^4)dx+(5x^3y^2-8xy^3)dy=0Homework Equations The Attempt at a Solution I've already tried the most logical steps. The equation isn't exact and I couldn't find an integrating factor to make it exact. It's also not homogeneous or separable. I have to be making an...

Dear All: Given two random variables X and Y, if I have established the relationship E[X]>=E[Y], does this necessarily imply that X must have a first-order-stochastic dominance over Y? I know that first order stochastic dominance implies that the mean value of the dominating random...

Can this second order be changed into a system of first order: $$ x''(t) = -\frac{\mu}{(\sqrt{x^2+y^2+z^2})^3}x $$

Here is the question: Here is a link to the original question: Solve this differential Equation: df/dy(t) + f(y) =sin(2y)? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Hi, Wondering if anyone can give me some help with reducing this 3rd order ODE to a first order problem, so it can be written in the form u' = f(u, t) Homework Equations The 3rd order ODE is: x'''(t) + x''(t) + 2x'(t) + 2x(t) = 2t^2 + 4t - 5; The initial values...

I'd really appreciate help with two little questions relating to first order partial differential equations. Just to quickly let you know what I'm asking, the first is about solution methods t first order PDE's & pretty much requires you to have familiarity, by name, with Lagrange's method...

Homework Statement (y^2 + xy)dx - x^2dy = 0 The Attempt at a Solution Put it into derivative form. y^2 + xy - x^2 \frac{dy}{dx} = 0 \frac{dy}{dx} - \frac{y^2}{x^2} - \frac{xy}{x^2} = 0 \frac{dy}{dx} + \frac{-1}{x}y = \frac{1}{x^2}y^2 I recognized this as a Bernoulli equation...

Homework Statement Solve the following differential equation: y*e^(x^2)*dy/dx=x+xy Homework Equations y'+P(x)*y=Q(x) The Attempt at a Solution I tried to modify the equation to match the first order linear one, and I got: e^(x^2)*dy/dx=x/y+x (divided everything by y), but...

Homework Statement Solve the initial value problem: t(dy/dt)+8y=t^3 where t>0 and y(1)=0 Homework Equations None? The Attempt at a Solution It's a linear equation, so rearranged to dy/dt+8y/t=t^2. Took the integrating factor e^(∫8/tdt)=t^8 and multiplied through...

The problem is : dy/dx=(x(x^2+1))/4y^3 when y(0)=-1/√2 This is my work so far: ∫4y^3dy=∫x(x^2+1)dx (y^4)/2=((x^2+1)^2)/2+c The answer from the textbook is y=-(√(x^2+2)/2) As you can see, my work will never equal the textbook answer when you put it in the y= stuff form. What did I do wrong?

Given an open connected subset D of the (t,x) plane and a function f\in C(D,\mathbb{R}), we say \varphi\in C^1(\text{proj}_1D,\mathbb{R}) is a solution of the first order differential equation x'=f(t,x) if and only if \forall t\in \text{proj}_1D,\quad (t,\varphi(t))\in D and \forall t\in I...

Hi all, Just a few question about FOL logic. What is the difference between terms and atoms, I read lot's of differents definitions, then when I think that I've understood, I find an exemple where both are used without any difference (for ordering by instance). An another question is : What...

Hi. For first order system ODE, complex root. y'=Ay, where A is a 2by2 matrix. I am assuming the roots are complex. After finding the eigenvalue (complex conjugate) and their eigen-vectors (which come in a form of complex conjugate again), we plug into the solution y=ζexp(λt), where λ is...

Using z = y/x to transform the given homogeneous differential equation into a differential equation in z and x. By first solving the transformed equation, find the general solution of the original equation, giving y in terms of x. z = \frac{y}{x} \rightarrow y = xz \rightarrow \frac{dy}{dx} =...

solve dy/dx = x(1-x) I got y = (x^2)/2 - (x^3)/3 + C however in the solutions they've gotten: where did t come from?

I'm not sure what happens when you replace the inductor with a short circuit. The current source is what throws me off. One thought I had was that you can remove the 6 and 2 kohm resistors, but then I don't know what ahppens to the current source. http://imgur.com/lks7y Thanks

Homework Statement Find an integrating factor for the first order linear differential equation \frac{dy}{dx} - \frac{y}{x} = xe^{2x} and hence find its general solution Homework Equations The Attempt at a Solution I found the integrating factor which is e^{-lnx} = x^{-1} and...

Hi! I'm trying to learn the Feynman rules trough Wick's theorem right now and I'm focusing on QED. Here the first order term of the S-operator can be written as -ie\int d^4x :\bar \psi(x) \gamma^\mu \psi(x) A^\mu(x): but the author of the book I'm reading (Greiner Reinhart) claims that all...

Homework Statement The current in a 25mH inductor is known to be - 10A for t <= 0 and (-10cos400t - 5sin400t)e^-200t A for t >= 0. Assume the passive sign convention. Part A: At what instant of time is the voltage across the inductor maximum? Part B: What is the maximum voltage...

Homework Statement I'm having a hard time to solve the following DE using an integrating factor, I'm asked to find one and solve the DE. (x+y^2)-2xyy'=0.Homework Equations The Attempt at a Solution If I call u=u(x) (I assume the integrating factor depends only on x, not on y), the following...

Hi Everyone I tried all ways I can to solve (y^2+x^2+x)y'-y=0, but still cann't find a way to solve it. Could anybody help on it? Thank you very much!

Homework Statement How were the integral lines dt/a = dx/b derived from the PDE aUt + bUx = 0 where Ut is the partial derivative with respect to time and Ux with respect to x and a, b are constants. Homework Equations I honestly have no idea. I may be unprepared for this course as...

1. how do i solve X'(t)=A(t)X(t) Homework Equations I know of this equation: x(t) = x_0 \exp\left( \int_{t_0}^t f(\xi) \, d\xi \right) but i think that I'm using it wrong. The Attempt at a Solution i have the following mathematica code: A= x = MatrixExp[Integrate[A, {t, 0, s}]].{1, 0,0,0}...

Just a quick question for you people - If I have a linear RLC series circuit where there is an uncharged capacitor at time t=0, and the switch is closed, is it an entirely different analysis (in terms of laplace transforms) than If, say, the some battery charges a capacitor, then I put it into...

Behaviour of any first-order circuit can be described by a first-order ordinary differential equation (often called the state equation) of the form : dx/dt + αx = βy(t); x(0) = x0 where x is the state variable (usually the voltage across a capacitor or the current across an inductor), y(t) is...

Homework Statement x\frac{dy}{dx} = 4yHomework Equations I'm not sure if there is a specific equation for these type of problems. My professor just says to separate the two different variables and then integrate them with respect to x.The Attempt at a Solution \frac{1}{4y} \frac{dy}{dx} =...

Homework Statement uploaded file (Problem 5)Homework Equations uploaded fileThe Attempt at a Solution Ok so I think I have the correct answer but the problem is I don't know how to solve for the actual answer with 2 equations which one do I plug into? Sorry for all the erasing!

Homework Statement A culture of bacteria have a growth rate (as a percent) given by kb per year, constant k>0 and b is the number of bacteria. A virus removes bacteria at a rate of m bacteria per year. I am trying to model this information using an ODE, but might be making a mistake. Homework...

Homework Statement Solve this first order linear ODE x (dy/dx)-2y=6x5Homework Equations The Attempt at a Solutionx (dy/dx)-2y=6x5 divide through by x dy/dx -2y/x = 6x4 I= e∫-2/x dx =e-ln(2) =-2 ∴ -2(dy/dx) + 4y/x = -12x4 d/dx(-2y) = -12x5/5 + C y= 6/5(x5) - C/2 this is wrong but...

I am trying to solve: (x + 1 + f(-x) )(1 - f ' (x) ) = x+1 f(0) = x_0 x in (-1,1) I approximated it numerically but any analytic method I try fails. Any ideas?

Homework Statement Verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit solution y=∅(x) in each case.Homework Equations \frac{dX}{dt}=(X-1)(1-2X); ln(\frac{2X-1}{X-1})=t The Attempt at a Solution I know I need...

Homework Statement I want to find the general solution for y(x) if dy/dx = x + y^2 with initial cond't y(1) = 2 Homework Equations The Attempt at a Solution I can't figure out how to make it linear. (Obviously I don't think it's seperable) Any suggestions/solutions...

Find the first order partial derivatives of the function x = f(x,y) at the point (4,3) where: f(x,y)=ln|(x+√(x^2+y^2))/(x-√(x^2+y^2))| I understand the method of partial derivatives and implementing the given point values once the partial derivatives are found, however I am having trouble...

Hi all, got a Control question here, and I'm struggling with what I assume is a simple algebraic step. Thanks in advance! Homework Statement A closed loop control system governs the level of water in a tank (H(s)) to meet a target height (Hi(S)). The flow of water into the tank is controlled...

hello world, I've been doing some summertime training to brush up my math skills and have been struggling with this [dy]/[/dt]=(4exp(-y)+const*exp(-2y))^1/2 In fact this is the simplified version of a Bernouilli equation. I know that it is separable, I'm just struggling with the...

Ok so I have a classic particle in a box problem. If a particle in a box, the states of which are given by: ψ = (√2/L) * sin(nπx/L) where n=1,2,3... is perturbed by a potential v(x) = γx , how do I calculate the energy shift of the ground state in first order perturbation I'm guessing that...

hi the differential equation i am attempting to solve is: \frac {dP} {dx} = \frac {gP} {1+P/Psat} here is what I have done: \frac {dP} {dx} = \frac {gP*Psat} {Psat+P} divide both sides by \frac {Psat+P} {gP*Psat} to get: \frac {Psat+P} {P*Psat} \frac {dP} {dx} =g...

Hi, Look at \begin{align} & \int d^4 x d^4 x_1 d^4 x_2 d^4 x_3 d^4 x_4 \exp [i(p_1 x_1 + p_2 x_2 -k_1 x_3 -k_2 x_4)] \\ & \times (-i\lambda)D(x_1-x)D(x_2-x)D(x_3-x)D(x_4-x) \end{align} for first order in lambda for 2-2 scattering. In Maggiore I am told to substitute y_i=x_i-x as a...

I am trying to solve four coupled equations. Three of them are first order differential equations and the fourth is a algebraic one. The equations look something like this: V_{l}(r) = f_{1}(r)W'_{l}(r) (1) h''_{l} + f_{2}(r)h'_{l} + f_{3}(r)h_{l}(r) = U_{l}(r) (2) f_{4}(r)U'_{l} +...