First order Definition and 546 Threads

Hello, I am trying to solve the following integral (limits from 0 to inf). ∫j_1(kr) dr where j_1 is the first order SPHERICAL Bessel function of the first kind, of argument (k*r). Unfortunately, I cannot find it in the tables, nor manage to solve it... Can anybody help? Thanks a lot! Any...

Hi, I have problems rewriting equations with the term y'' as a system of first order differential equations. I've been given several equations and was told to write them as 1st order DEs, then calculate the numerical solution using the Euler's modified method. I know that y'=f(x,y), so if...

Hi there. This is my first time working with tensors, so I have to break the ice I think. I have this exercise, which I don't know how to solve, which says: If V=V_1...V_n is a first order covariant tensor, prove that: T_{ik}=\frac{\partial V_i}{\partial x^k}-\frac{\partial V_k}{\partial x^i}...

Homework Statement Solve y^2*(1-(dy/dx)^2)=1 Homework Equations The Attempt at a Solution I expressed the ODE in terms of dy/dx and considered two cases. I got (a) y^2 = 1 + (x+C)^2 (b) y^2 = 1 + (-x+C)^2 where C is a constant However, my professor told me that there is...

Hello. I have simple DE y' + p y^(1/2) = q --------------- y'=dy/dt p,q=constant I am confused because I tried bernoulli's method to solve and I think I exploded the universe. Basically, my initial condition of t=0,y=0 made infinity, not right. I'm not sure that method works when there...

Hi there: I am trying to solve a two points boundary value problem. Consider a function f:[x1,x2]->[x2,x3] x1 and x3 are knowns x2 is an unknown parameter f'(x) = exp( -a*x + b*f(x) ) where b>a>0 Two boundaries conditions: f(x1) = x2 f(x2) = x3 Does anyone know how to...

Solve $u_x+2u_y+2u=0,$ $x,y\in\mathbb R$ where $u(x,y)=F(x,y)$ in the curve $y=x.$ I don't know what does mean with the $y=x.$ Well I set up the following $\dfrac{dx}{1}=\dfrac{dy}{2}=\dfrac{du}{-2} ,$ is that correct? but I don't know what's next. Thanks for the help!

How do you solve (analytically or numerically) a differential equation of this form, $$\frac{\mathrm{d}y(x)/\mathrm{d}x}{\mathrm{d}z(x)/\mathrm{d}x} = a[1-y(x)-z(x)] + b$$ where a, b are constants. Also, $$y(0) = z(0) = 0$$

Homework Statement Question According to Newton’s Law of Cooling, the rate at which a substance cools in air is proportional to the difference between the temperature of the substance and that of air. The differential equation is given byAccording to Newton’s Law of Cooling, the rate at which...

Homework Statement \frac{dy}{dx} = y \sqrt{x} , f(9) = 5 The Attempt at a Solution \int dy/y = \int \sqrt{x} dx ln |y| = \frac{2}{3} x^\frac{3}{2} + c y = e^{\frac{2}{3}x^\frac{3}{2}} + C y = Ce^{\frac{2}{3}x^\frac{3}{2}} 5 = Ce^{\frac{2}{3}9^\frac{3}{2}} 5 =...

Homework Statement http://imgur.com/VsDrQ,dJ2iv Homework Equations Current in loop 1: i_1 going counter-clockwise Current in loop 2: i(t) going counter-clockwise Before opening switch: we know that 2 loops exist, left and right. also the current is constant because it says the...

I feel as if I have made the correct substitution, what am I missing? See Attachment. Thanks, Dane

Homework Statement solve the differential equation: (1+t^2)y'+4ty=(1+t^2)^-2Homework Equations μ=exp∫adt The Attempt at a Solution this problem gets quite ugly, so here goes. first question does μ=e^(1+t^2)^2

3y'+2y-2sin(3x)+2e(-3x)+x3+4=0 Variables x - independent y - dependent Attempt at a solution I rewrote the equation in form dy/dx+P(x)y=Q(x) and used an integrating factor of \mu(x)=ke(2/3)x with P(x) = 2/3 and Q(x) = 2sin(3x)-2e(-3x)-x3-4 Since y(x) =...

1) $u_x+u_y=0,\,x\in\mathbb R,\,y>0$ and $u(x,0)=\cos x,\,x\in\mathbb R.$ 2) $xu_x+u_y+uy=0,\,x\in\mathbb R,\,y>0$ and $u(x,0)=F(x),\,x\in\mathbb R.$ 3) Solve the following equation $2xu_y-u_x=4xy,$ where the initial curve is given by $x=0,\,y=s,\,z=s.$ ------------------------- 1) Laplace...

Solve $u_y+f(u)u_x=0,$ $x\in\mathbb R,$ $y>0,$ $u(x,0)=\phi(x).$ What's the easy way to solve this? Fourier Transform? Laplace Transform?

The problem and attempt at solution are typed below

For example: \frac{dy}{dx} + y = e^{3x} I understand that these differential equations are most easily solved by multiplying in a factor of integration, and then comparing the equation to the product rule to solve et al.. For example: t\frac{dy}{dx} + 2t^{2}y = t^{2} \frac{dy}{dx} + 2ty = t...

Homework Statement dy/dt=y((3t^2)-1), y(1)=-2 Homework Equations Basic integrals The Attempt at a Solution integrate on both sides: dy/y=dt((3t^2)-1) ========>ln(y)=(t^3)-t+c ========>y=e^((t^3)-t+c) ========>y=e^((t^3)-t)e^(c) I am not sure if its some e rule that I forgot...

Homework Statement Assume there is a voltage source in series with a resistor and a capacitor. Thus, V_S=i(t)R+v_C(t)=CR\frac{dv_C}{dt}+v_C\rightarrow{}dt/(RC)=dv_C/(V_S-v_C) From this point I understand that one has to apply a negative sign to both sides before integrating, but why is it...

Suppose we have some ODE given by y' = G(x,y)/H(x,y). Let x and y depend on a third variable, t, so that x and y are parametrized in a way. Then applying the chain rule to y' gives \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{G(x,y)}{H(x,y)} Then comparing the numerators and...

How can i differentiate between first order & second order ??!

Homework Statement I need to solve this DE system for a lab: q_1'=2-\frac{6}{5}q_1+q_2 q_2'=3+\frac{3}{5}q_1-\frac{3}{2}q_2Homework Equations The Attempt at a Solution I know how to use the method of elimination to solve such systems, but this is non homogeneous because of the added constant...

Hi, I am not sure it is the right subcategory to post a question on statistical physics. But anyway, I read a couple of times that adding a m^3 to the Landau free energy implies that we may observe a first order transition phase, but I don't see why. Maybe it does imply some discontinuity in...

Hello, I have a problem in the form \frac{\partial u}{\partial t}+\frac{\partial u}{\partial x}+e^{x}u=0 with conditions u(x,0)=u_0(x) u(0,t)=\int_{0}^{\infty}f(x)u(x,t)dx Im confused, because in first order PDE i require only 1 condition. How to solve this for two conditions?

I have derived a first order nonlinear PDE with its corresponding initial and boundary conditions given by: dv/dt + A*(v^2)*dv/dx = 0 (where A is a constant) v(t = 0) = C (constant value) v(x = 0) = 0 I'm not quite sure how to solve this. I was thinking about using the method of...

Homework Statement Solve the first order difference equation. Homework Equations x[n] - x[n-1] = n(n+1)/2 x[1] = 1 The Attempt at a Solution Homogenous solution: Characteristic equation: r - 1 = 0 <=> r = 1 => yhn = C * 1^n = C Particular solution: ypn = ? I'm supposed to...

Homework Statement Systems of first order equations can sometimes be transformed into a single equation of higher order. Consider the system (1) x1' = -2x1 + x2 (2) x2' = x1 - 2x2 Solve the first equation for x2 and substitute into the second equation, thereby obtaining a second order...

Please teach me this: Why the Lagrangian in QFT does not include high order derivative of field?Is it correct the reason being all fields obey the only Dirac and Klein-Gordon equations? Thank you very much for your kind helping.

Homework Statement Find all solutions to [dx/dt; dy/dt] = [1, 2; 0, 1]*[x; y] Homework Equations the eigenvalue characteristic equation: det(A-λ*I)=0 The Attempt at a Solution This results in real, repeated eigen values: λ1,2 = 1 for λ1 = 1, (1-1)k1 + 2k2 = 0 choose k1 =...

The problem: dx(1-y^2)^1/2=dy(1-x^2)^1/2 y(0)=3^(1/2)/2 My attempt: I separated the variables and integrated, and came up with sin^-1(x)+c=sin^-1(y) This is where i am stuck. any suggestions? did I run astray anywhere?

I am asked to find the general solution to: \dfrac{dy}{dx}\sin x + y \sec x = \cos^2 x I don't quite know where I am going with this one; by simply looking at it, I can't seem to see what I would differentiate in order to get the left side and equally, I don't know if dividing through by...

How to solve this differential equation? dy/dx = - (3yx^(2) + y^(2)) / (2x^(3) + 3xy) I've tried finding an integrating factor in order to make it exact, but I don't know what to do with this. The answer is given as x^(3)y^(2) + xy^(3) = c I'm so confused. I separated it...

Homework Statement Find the orthogonal trajectories of the given families of curves. x^2 + y^2+2Cy=1 Homework Equations The book has covered homogeneous and separable methods.The Attempt at a Solution To find the orthogonal trajectories, we simply find the curves whose tangents are...

Homework Statement The dynamic behavior of a pressure sensor/transmitter can be expressed as a first-order transfer function (in deviation variables) that relates the measured value Pm to the actual pressure, P: Pm'(s)/P'(s)=1/(30s+1). Both Pm' and P' have units of psi and the time constant...

i have this differential equation of the first order [x^2+y^2]+[2xy+y^2+(x^3/3)]dy/dx=0 i tried to solve it by substitution putting x^2+y^2=v ,but it doesn't work also it is not exact or homogeneus to solve it by these methods. I still believe it can be solved using substitution but i can't...

Homework Statement Solve the following DE: 2xyy'=4x^2+3y^2. Homework Equations Bernoulli's DE: y'+P(x)y=Q(x)y^2. The Attempt at a Solution I know that the original DE isn't under Bernoulli's form, but I have thought a lot on the problem and my feeling is that if I could find a...

Homework Statement I must solve the following DE: x+y+1+(2x+2y-1)y'=0. I can't write the DE under the form y'+P(x)y=Q(x) so I can't use the integrating factor method. I checked out of the DE is exact, and it's not.Homework Equations Not really sure.The Attempt at a Solution I tried a...

Hi there, I've having problems solving a particular nonlinear ODE. Any help/suggestions will be highly appreciated. The nonlinear ODE is: v[t]*v'[t] + (4*v[t])/(t^2 - 1) = t/(t^2 - 1) Thank you.

My book stated the following theorem: If the functions P(x) and Q(x) are continuous on the open interval I containing the point x0, then the initial value problem dy/dx + P(x)y = Q(x), y(x0)=y0 has a unique solution y(x) on I, given by the formula y=1/I(x)\intI(x)Q(x)dx where I(x) is the...

Homework Statement Find the following IVP Diff.Eq. xyy'=x^2+3y^2 y(1)=2 Homework Equations The Attempt at a Solution I've been struggling with this problem for a while now. I believe I have figured out it is homogenous, thus y=ux substitution applies. Through some work I have arrived at...

Let us consider the following partial differential equation: {(}\frac{\partial z}{\partial x}{)}^2{+}{(}\frac{\partial z}{\partial y}{)}^{2}{=}{1} ---------- (1) The general solution[you will find in the texts: http://eqworld.ipmnet.ru/en/solutions/fpde/fpde3201.pdf is given by...

Homework Statement Hi, I am trying to work through exercise 2.1 on page 37 of Microcavities (by alexy kavokin, jeremy baumberg, guillaume malpuech and fabrice laussy) the problem is to prove | g^{(1)}(\tau) | = | cos( \frac{1}{2}(\omega_1 - \omega_2)\tau) ) | where...

Hi All, I have been trying to solve following nonlinear differential equation, but I couldn't solve it. 0 = a*[f(t)]^{z/(z-1)} + (-t+C)*f(t) + b*[df(t)/dt] where a, b and C are constants and 0< z<1. Could you please help me how to solve this nonlinear differential equation? I would...

Homework Statement I haven't done this for several years and have forgotten. Kicking myself now over it since it looks like something so simple but i cannot figure it out... I need to break this second order ODE into a system of first order ODE's in matrix form to use within a crank...

Homework Statement Solve the initial boundary value problem: u_t + cu_x = -ku u is a function of x,t u(x,0) = 0, x > 0 u(0,t) = g(t), t > 0 treat the domains x > ct and x < ct differently in this problem. the boundary condition affects the solution in the region x < ct, while...

The question is x^2dy/dx + y^2=0 , y(1)=3 I re-arrange the equation to get -1/y^2dy=1/x^2dx Seperated them, then I integrate both sides to get 1/y=-1/x + c Now I don't get how they got the answer y=3x/(4x-3), as when I try use the condition I get a different answer, could anyone help? I...

Hello. Is there any way to build a band reject filter ('notch') whose transfer function, H(s), has only two complex zeros and only one real pole? For example: H(s) = \displaystyle\frac{s^2+4}{s+1000}

Hi I have a set of two linearized integro-partial-differential equations with derivatives of first order (also inside the integrals). How many boundary (initial) conditions should I give for such problem for the solution to be unique? is the 'initial condition that intersect once with the...

I'm trying to solve the following ODE: ydx+(\frac {e^x}{y}-1)dy=0 I tried to transfer this ODE into exact form but no luck. Will appreciate any help.