First order Definition and 546 Threads

Homework Statement Consider the first order differential equation \frac{dx(t)}{dt} + ax(t) = f(t), x(0) = x_{0}, t\geq0 Suppose the "input signal" f(t)=e^{-t}, t\geq0 . (a) Find the solution to the equation. Find a condition on the parameter a so that the solution of the (forced) system...

Hey there, first post here! I've been struggling with a detail in Second Quantization which I really need to clear out of my head. If I expand the S-matrix of a theory with an interaction Hamiltonian H_I(x) then I have S - 1= \int^{+\infty}_{-\infty} d^4 x H_I(x) +...

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

Homework Statement Hello, I was given an extension problem in a Dynamics lecture today and am struggling to solve it. It is a simple scenario: a particle of mass m is accelerating due to Galilean gravity, but is subject to a resistive force that is non-linear in the velocity of the particle...

How to proceed to find the general and singular solution of the equation 3xy=2px2-2p2, p=dy/dx

Kindly solve it and i need help to understand NON LINEAR Questions

First order in time=>"time cannot go backwards"? I have had numerous professors mention, but not explain, the differences between PDEs that are second order and first order in time. For example, in the regular wave equation, they say that "time can go backwards," or something to that effect. In...

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

Homework Statement Find the general solution of 2y' + y - (2y')*ln(y') = 0 Homework Equations The Attempt at a Solution I have no idea how to deal with this i mean none of the first order techniques work and it's mainly because I don't know how to deal with the ln(y'). I tried seperating...

Homework Statement Mod note: Pasted the OP's correction into the original problem.[/color] Solve xe^z\frac{\partial u}{\partial x} - 2ye^z\frac{\partial u}{\partial y} + \left(2y-x \right)\frac{\partial u}{\partial z} = 0 given that for x > 0, u = -x^{-3}e^z when y=-x Homework Equations...

Could someone please provide a worked solution for me. I think that is the only way I will understand this. It was covered very vaguely in our lectures and my notes start talking about vectors and using co-domain notation which is very frustrating! 1. $y''(x) = x + y'(x) + e^{y(x)}$ with...

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

Here is the question in attachment , I make it as the site don't support LaTeX I think! https://www.physicsforums.com/attachment.php?attachmentid=63439&stc=1&d=1383093152

Find the gernal solution of cosx\frac{dy}{dx}+(sinx)y=1 So \frac{dy}{dx}+\frac{sinx}{cosx}y=\frac{1}{cosx} \frac{dy}{dx}+tan(x)y=csc(x) therefore P(x)=tan(x) Let \mu (x) = e^{\int P(x) dx}=e^{\int tan(x) dx} =\frac{1}{cosx} multiply both sides of the equation by integrating factor...

Hello people, I couldn't solve the given D.E by using exact d.e & substitution method :( Thanks in advance. (x*y*sqrt(x^2-y^2) + x)*y' = (y - x^2*(sqrt(x^2-y^2) ) gif file of d.e can be found in the attachments part.

Good day. I was wondering if you could help me solve this first order linear partial differential equation: [∂δ]/[/∂t] = [ρg]/[/μ] δ^2 [∂δ]/[/∂z]. The solution for this is: δ(z, t) = √[μ z]/[/ρg t]. I don't really understand how the PDE became like this. If you could show the...

Hello, according to my textbook, the Taylor expansion of first order of a scalar function f(t) having continuous 2nd order derivative is supposed be: f(t) = f(0) + f'(0)t + \frac{1}{2}f''(t^*)t^2 for some t^* such that 0\leq t^* \leq 1 Quite frankly, I have never seen such a formulation...

Homework Statement Solve \frac{\partial{w}}{\partial{t}} + c \frac{\partial{w}}{\partial{x}} =0 \hspace{3 mm} (c>0) for x>0 and t>0 if w(x,0) = f(x) w(0,t) = h(t) Homework Equations The Attempt at a Solution I know how to solve for the conditions separately and that would give...

Hello, can you guys help me please with this differential equation from Demidovitch book, is to find the solution transforming to polar coordinates :

I'm having trouble with this problem... I am almost certain that I have the first part correct which is solving the first order DiffEQ using an integrating factor. I think that I am computing the constant incorrectly. I have followed all steps, including the similar problem given on WileyPlus...

Homework Statement Find the general solution to the following differential equation. dy/dx = 2x( (y^2) + 1) Homework Equations The Attempt at a Solution I got all x terms on one side and all y terms on the otherside 2x dx = 1/( (y^2) + 1`)dy integrate x^2 + c =...

A particle of mass m is subject to a force F(v) = bv^2. The initial position is zero, and the initial speed is vi find x(t) so far m*dv/dx*v = -bv^2 m*dv/dx = -bv integral m/-bv*dv = integral dx m/-b*ln(v) + a = x + b What do I do with the constants? i thought i was suppose to put...

Verify the indicated function y=phi(x) is an explicit solution of the given equation. Consider the phi function as a solution of the differential equation and give at lease one interval I of definition. (y-x)y'=y-x+8 where y=x+4\sqrt{x+2} So the derivative is y'=1+\frac{2}{\sqrt{x+2}} and the...

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

Homework Statement y'+ycot(x)=cos(x) Homework Equations The Attempt at a Solution First I found the integrating factor: \rho (x)=e^{\int cot(x)dx}=e^{ln(sinx)}=sinx Plug into the equation for first order DE... \int \frac{d}{dx} ysinx=\int cosxsinx dx End up with...

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200L of dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 L/min, the well-stirred solution...

Hello there, I have 3 sentences. They are: 1) If someone is not in the class then that person is either ill or lazy. 2) Ill people do not go for shopping. 3) The class teacher noticed that James is not in the class but she has seen James come out of the Candy...

Homework Statement Assume that there is a deviation from Coulomb’s law at very small distances, the Coulomb potential energy between an electron and proton is given by V_{mod}(r)=\begin{cases} -\frac{e^{2}}{4\pi\varepsilon_{0}}\frac{b}{r^{2}} & 0<r\leq b\\...

Homework Statement Solve using separation of variables utt = uxx+aux u(0,t)=u(1,t)=0 u(x,0)=f(x) ut=g(x) The Attempt at a Solution if not for the ux I'd set U=XT such that X''T=TX'' and using initial conditions get a solution. In my case I get T''X=T(aX'+X'') which is...

Homework Statement I required to make a perturbation expansion in ε of the function: Homework Equations A(X,y,z)=A(x-εsin(wy),y,z). X=x-εsin(wy) The Attempt at a Solution Solution: A(X,y,z)=A0(X,z)+ε[A1(X,z)+∂/∂XA0(X,z)]sin(wy)+o(ε^2) I get the terms A0(X,z) and ∂/∂XA0(X,z)sin(w,y) with the...

Homework Statement Car Dynamics f(t)→ \frac{\frac{1}{M}}{s+\frac{D}{M}}→y(t) Applied Force Velocity Homework Equations M=1,000 kg and D=1000 kg/s Where f(t) represents the input force and y(t) is the output velocity. M is the Mass and D...

Homework Statement Homework Equations vc(t) = vc(∞) + [vc(0+) - vc(∞)]*e-t/τ (Voltage in a driven RC circuit) τ = RC (time constant for an RC circuit) The Attempt at a Solution I'm pretty shaky with these sorts of problems and am quite unconfident of my work here. Step...

Hey guys, I'm really interested in finding out how to deal with differential equations from the point of view of Lie theory, just sticking to first order, first degree, equations to get the hang of what you're doing. What do I know as regards lie groups? Solving separable equations somehow...

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

Hello MHB, $$(x^2+1)y'-2xy=x^2+1$$ if $$y(1)=\frac{\pi}{2}$$What I have done: Divide evrything by $$x^2+1$$ and we got $$y'-\frac{2xy}{x^2+1}=1$$ we got the integer factor as $$e^{^-\int\frac{2x}{x^2+1}}= e^{-ln(x^2+1)}$$ Now I get $$(e^{-ln(x^2+1)}y)'=e^{-ln(x^2+1)}$$ and this lead me to...

Hi I am trying to solve dy/dx = 3x^2-2x+2+(8/x *y) Can anyone show me how to rearrange to standard form as I am mightly confused :(

Here is the question: Here is a link to the question: Can someone help me solve this: y'+tan I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: Homogenous Differential Help with equation? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement dy/dt = k*y*ln(y/M), where M and k are constants. Show that y = Meaekt satisfies the above equation for any constant a. Homework Equations y' = ky y = P0ekt The Attempt at a Solution Taking the derivative of y, I get: (Meaekt)*(aekt)*k which is, ky*aekt ..and I'm...

Hi! I'm having a lot of trouble solving the following ODE: dx/dt = A - B*sin(x) where A and B are constants. My ODE skills are a bit rusty, and I wasn't able to find anything on the Internet that could help me, so could someone please show me how to solve for x in terms of t? I've...

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...