Differential Definition and 1000 Threads

$y(x^3e^{xy}-y) \, dx+x(xy+x^3e^{xy}) \, dy=0$ change it into exact differential and help me in solving it

Homework Statement I think there may be something wrong with a problem I'm doing for homework. The problem is: Solve the IVP with the differential operator method: [D^2 + 5D + 6D], y(0) = 2, y'(0) = \beta > 0 a) Determine the coordinates (t_m,y_m) of the maximum point of the solution as a...

Hi, I'm currently studying to become a chemical engineer. After learning differential equation and linear algebra, I've realized how useful they are in my engineering courses since they make setting up equations and solving them so much easier. So I was wondering if there are other math that...

1. Homework Statement It's to do with mirages, but I don't think the physics context is too important. It's also possible that the solution doesn't involve differential equations, and my method is completely wrong. I've been given that: ##A = \frac{n(1+ay)}{ sqrt(1+(y')^2)}## where y' is...

Homework Statement Hi there. I have a simple RC circuit with a battery voltage of 10 V, R = 1 Ω, C = 1 F and a switch. I want to use the Explicit Euler (forward divided difference) to solve the equation and check for stability, rather than using a ODE. I am finding the equation for when the...

Homework Statement Hi, basically I have a boundary value problem and just want to check that my general solution is correct. x'''' + 16x = 0 Homework EquationsThe Attempt at a Solution I'm pretty sure you make a characteristic equation which would be m4 + 16 = 0. Solving this I get m to be...

Euler mentions in his preface of the book "Foundations of Differential Calculus" (Translated version of Blanton): I don't understand here, who/who all had invented/discovered the study-of-ultimate ratio (differential calculus) for rational functions long before (Newton and Leibniz), without...

Hi evry body i would like to have an help to resolve this exercice below the followin differential equation with its initial condition dy/dt=-lambda t y(t) t>=0 avec y(0)=y0 where lambda is damping coeficient strictly positive. -find the solution of this equation with Euler's explicite and...

Homework Statement Given u(x.y), find the exact differential equation du = 0. What sort of curves are the solution curves u(x,y) = constant? (These are called the level curves of u). u = cos(x2 - y2)The Attempt at a Solution partial derivative du/dx = (-2x)sin(x2 - y2)dx partial derivative...

Homework Statement A simple electrical circuit consists of a voltage source E(t) = t*e-t volts, a resistor R = 1 and an inductor L = 1/10 H connected in series. It is assumed that I(0) = -10/81 a) The differential equation that governs the current I (t) in this circuit . b) Find the time...

Homework Statement equation (1) y' + (ylny)/x = xy we set y(x)= eu(x) Equation (1 ) proposed becomes an equation 1st order linear differential type : equation (2) u ' + p( x) u = q ( x) a) Find the equation ( 2) using the change of variable proposed above. Homework EquationsThe Attempt at a...

Euler was the master in analysisng anything. This can be seen in his words in the preface of his book "Mmathematica" (translated by Ian Bruce), where he speaks on the text of Hermann "Phoronomiam": Euler has given many insightful words on analysisng things in his preface of many other books...

Homework Statement A block of mass m, which has an initial velocity v0 at time t = 0, slides on a horizontal surface. If the sliding friction force f exerted on the block by the surface is directly proportional to its velocity (that is, f = -kv), A) Write a differential equation for the...

Homework Statement Find the general solution to the equation. Homework Equations (dy/dx) - y - e^3x=0 The Attempt at a Solution [/B] I rewrote this as dy/dx - y = e^3x This is a linear first order ODE, in the form dy/dx + P(x)y = f(x) P(x) = 1; f(x) = e^3x The integrating factor =...

So I'm not sure whether this should be posted in the Physics forum or not, but here goes: I'm a Junior ME student at NC State taking a Vibrations course. We've gone over the general differential equation for mass-damper-spring systems where Meq⋅x'' + Ceq⋅x' + keq⋅x = Fextermal What I was...

Homework Statement dNa/dt = -Na/Ta where Na is the function and Ta is the constant dNb/dt = Na/Ta - Nb/Tb where Nb is the function and Tb is the constant Homework Equations My Prof said Nb(t) has the form Nb(t) = Cexp(-t/Ta) + Dexp(-t/Tb) The Attempt at a Solution I know the first equation...

Dear all I am studying general relativity and i have a question as follow. We have the 2- sphere can be scanned totally by a coordinate system (theta, phi) with the metric tensor written in terms of theta and phi. Now i want to divide the 2-sphere into charts 4 charts then each will have its own...

Homework Statement Hello everyone, I need to find K for the following differential equation to be exact. (y3+kxy4-2*x)dx +(3xy2 +20x2y3)dy=0 Homework EquationsThe Attempt at a Solution (y3+kxy4-2*x)dx +(3xy2 +20x2y3)dy=0 dM/dy = d/dy(y3+kxy4-2*x) = 4*k*y3*x+3*y2 dN/dx =d/dx(3xy2 +20x2y3) =...

Homework Statement I need to resolve this with v = y/x dy/dx= (3y2-x2)/(2xy) Homework EquationsThe Attempt at a Solution dy/dx= (3y2-x2)/(2xy) dy/dx= 3y2/2xy -x2/2xy dy/dx = 3y/2x -x/2y dy/dx = 3y/2x - 1/2y/x dy/dx = 3/2 *v - 1/2*v F(v) = 3/2 *v - 1/2*v is that good so far ?

Homework Statement Homework Equations F=ma ac=v^2/r f=uN v=v0+at w=v/r The Attempt at a Solution v=v0+at v=vo+umv^2/r v^2(u/r)-v+vo=0 I don't see what differential equation i could use since the speed is dependent on the friction (equal to friction coeff times centripetal force) which in...

Hi guys, I was browsing in regards to differential equations, the non-linear de and came up with this site in facebook: https://www.facebook.com/nonlinearDE Are these people for real? Can just solve any DE like that, come up with a series? Not an expert in this area, so I do not know what if...

Homework Statement Observe a Cauchy problem \begin{cases}y' + p(x)y =q(x)y^n\\ y(x_0) = y_0\end{cases} Assume ##p(x), q(x)## are continuous for some ##(a,b)\subseteq\mathbb{R}## Verify the equation has a solution and determine the condition for there to be exactly one solution. Homework...

Homework Statement http://imgur.com/goozE9f Homework Equations ##(dx_i)_p i= 1,2,3## 3. The Attempt at a Solution [/B] I'm reading Manfredo and Do Carmo's Differential Forms and Applications. This is the very first page Would you mind explaining me what is meant by dx, as highlighted in the...

I don't know if this is a silly question? Am I missing simple math? How does a wave depending on amplitude and frequency make it's equation a second order differential equation?

I'm trying to understand how the integral form is derived from the differential form of Gauss' law. I have several issues: 1) The law states that ## \nabla\cdot E=\frac{1}{\epsilon 0}\rho##, but when I calculate it directly I get that ## \nabla\cdot E=0## (at least for ## r\neq0##). 2) Now ##...

Hi, I have two coupled differential equations d^2 phi(z)/dz^2=lambda*phi(z)*(phi(z)^2+psi(z)^2-sigma^2) d^2 psi(z)/dz^2=lambda*psi(z)*(phi(z)^2+psi(z)^2-sigma^2+epsilon/lambda) where lambda, epsilon and sigma are arbitrary constants. The equation subject to the bellow boundary conditions...

Can anyone help me to solve a differential equation? I want to solve ∂v(p,t)/∂t=-p^2 v(p,t)-sqrt(2/pi)∫v(p,t)[1-δ(t)R(t)]dp+sqrt(2/pi)[δ(t)R^2(t) C] with initial data v(p,0)=0 where C is constant and the integration from zero to infinty Any suggestion please? Solution by volterra integral...

I'm studying General Relativity and Differential Geometry. In my textbook, the author has written ##x^2=d(x,.)## where d(x,y) is distance between two points ##x,y\in M##. I couldn't understand what d(x,.) means. Moreover, I am not sure if this is generally true to write ##x^2=g_{\mu\nu} x^\mu...

how do you solve this equation? y´´ + k/(y^2) = 0 ? I got it from applying Newton's 2nd law of motion to an object falling from space to Earth only affected by gravitational force. Thank you!

Solve the given differential equation by separation of variables. (dy/dx)= (xy+3x-y-3)/(xy-2x+4y-8) First, I noticed when i divided both sides by the left hand side and multiplied both sides by dx, nothing canceled or seemed to work. I got to thinking. on the right hand side I preformed long...

a) On January 1 2000, the park estimated that they had 500 deer on their land. Two years later, they estimated that there were 550 deer on the land. Assume that the number of deer was changing exponentially, i.e. P(t)=ae^bt where P is the number of deer at year t, and a and b are parameters.Find...

I am looking to pick up one of these texts, but I don't really want to buy all three. Is there a considered favorite? Thanks in advance. B. O'Neill: Semi-Riemannian Geometry with Applications to Relativity T. Frankel: The Geometry of Physics B. Schutz: Geometrical Methods of Mathematical Physics

Homework Statement dy/dx = 4e-xcosxThe Attempt at a Solution [/B] I've divided dx to both sides, and now have dy = 4e-xcosx dx I've then started to use intergration by parts to the right side with u = 4e-x and dv = cosx dx Leaving y = 4e-xsinx - ∫ -4e-xsinx dx Once again I used intergration...

Homework Statement dy/dx + 2sin2pix = 0 -------Answer: y = 1/pi cos2pix + c Homework EquationsThe Attempt at a Solution I made several attempts but no success to the correct answer. The first step I made was subtracting 2sin2pix to both sides. I then used integration by parts, and this is...

I know there are a number of ways to do this problem, to increment the series etc. but, would someone please be able to explain how they get the answers for this problem simply and easily ? Thanks! A screen shot is attached

this starts as a calculus question, but springs into where i can get help with david bachman's A GEOMETRIC APPROACH TO DIFFERENTIAL FORMS second edition. looking at paul's notes cheat sheets http://tutorial.math.lamar.edu/cheat_table.aspx we have## \int \frac{1}{\sqrt{a^{2}-x^{2}}} =...

Homework Statement Identify the following differential equation as linear, separable, exact, or a combination of the three. $$1 + \frac{1+x}{y}\frac{dy}{dx} = 0$$ Homework Equations Start with ##F(x,y)=C## ##\displaystyle \frac{d}{dx}(F(x,y)) = \frac{d}{dx} (C)## ##\displaystyle...

Solve y'' - 2y' + 2y = ## e^x tanx ## What concept should we use if we know only solving first order differential equation?

Hey! :o Could you give me some information about differential algebra? What is it about? Differential-algebraic equations (DAEs) are polynomials with complex coefficients and the unknown variables are $z, x, x'$. Is this correct? What is the difference between them and the ODEs? Two...

I'm having some difficulty with a problem from Boyce & DiPrima's Elementary Differential Equations and Boundary Value Problems, 9th Edition. The problem comes from Section 2.8: The Existence and Uniqueness Theorem and is part of a collection of problems intended to show that the sequence...

Let V1 be the voltage across C1 and V2 be the voltage across C2. I want to solve for V1 and V2 as a function of time. My idea was to use dV1/dt=I1/C1 and dV2/dt=I2/C2. Then using circuit rules i can express I1 and I2 as functions of V1 and V2 and substitute them into the previous diff eqs...

I am having a hard time understanding the conditions that set a plane to be called a region. According to definition 2.68, a set in the plane is called a region if it satisfies the following two conditions (p. 14): 1. "Each point of the set is the center of a circle whose entire interior...

I have been working on a math problem and I keep getting the some type of PDEs. x*dU/dx+y*dU/dy = 0 x*dU/dx+y*dU/dy+z*dU/dz = 0 ... x1*dU/dx1+x2*dU/dx2+x3*dU/dx3 + ... + xn*dU/dxn= 0 dU/dxi is the partial derivative with respect to the ith variable. Does anyone know about this type of PDE...

Homework Statement Homework EquationsThe Attempt at a Solution Any help would be appreciated

I'm in my last semester of my undergraduate majoring in mathematics (focusing on mathematical physics I guess - I'm one subject short of having a physics major) and am wondering, largely from a physics perspective if it would be better to do a functional analysis course or a differential...

The usual form for tension as a result of the symmetric Cauchy stress tensor is, $$\mathbf{t} = P \mathbf{\hat{n}}$$ or better $$t_i = {P_i}^j n_j$$ Buoyancy would be $$T = \int_{\partial V}{P_i}^j n_j da$$ integrated over a closed surface. I've assumed that the stress tensor ##P##, is, in...

Hi, I'm a beginner in mechanics so I need some help with a project I started. My project consists of a small kart-like car. The car will be Rear-Wheel-Drive and Rear-Engine too (RR layout). and I am willing to use a small 110cc moped engine. I have a trike Differential Gear for the rear shaft...

Homework Statement ##y' = \frac{cos x}{sin y}## ##y' = \frac{6x^2}{y(1 + x^3)}## Homework EquationsThe Attempt at a Solution So I was working through some textbook problems and there's something about the solutions of the above equations I don't quite understand. The first one: ##\int sin...

If z = e ^ (xy ^ 2), x = tcost, and y = tsint compute dx / dt for t = pi / 2 I kind of lost in this difficult question pls help I tried putting down the xy but using ln lnz = xy^2 Product rule? Or what. This is my first time encountering this kind of question

After a big mistake in this PF, I try to post my question here, hoping it is ok. I'm looking for a more "simple" relation than Darcy's law. I try to determinate what is the relation between air speed and differential pressure in a tube where there is a restrictor. A kind of relation like V=kP...