Differential equations Definition and 999 Threads

Could somebody help me to solve this really tough differential equations? \left( {x}{y} \sqrt{{x}^{2} - {y}^{2}}+{x} \right){y'}={y}-{x}^{2} \sqrt{{x}^{2}-{y}^{2}} Another tough one.I tried MATLAB which gave me sth about lambertW function which I haven't heard about before.Is there an...

Are all linear differential equations considered linear systems? Does the "linear" in both terms reference to the same characteristics? http://en.wikipedia.org/wiki/Linear_system http://en.wikipedia.org/wiki/Linear_differential_equation

Does the variable coeffcient in linear differential equations have to be polynomials? All the examples I have found seem to be polynomials for example the Cauchy–Euler equation. For example is sin(x)y'' + cos(x^2)y' + y = 0 still considered a linear differential equation with variable...

The original form: http://img190.imageshack.us/i/79624585.png/ http://img685.imageshack.us/i/70092098.png/ I have manged to get to (D + 1)x + (D2 +D +1)z = 0 but after that I am kind of lost.

Homework Statement a) What can you say about a solution of the equation y' = -y^2 just by looking at the differential equation? b) Verify that all members of the family y = 1/(x + C) are solutions of the equation in part (a) c) Can you think of a solution of the differential equation y' =...

Homework Statement Given a second order differential equation: y'' + P(x)y' + Q(x)y = 0 If y1(x) and y2(x) are linearly independent solutions of the DE, what form does Abel's Equation give for W(y1(x), y2(x))? If we assume that one solution y1(x) is known, what first order DE results from a...

Homework Statement "Show that each of the given differential equations of the form M(x,y)dx + N(x,y)dy = 0 are exact, and then find their general solution using integrating factors μ(x) = e∫h(x)dx and μ(x) = e∫g(y)dy Homework Equations (x2 + y2 + x)dx + (xy)dy = 0The Attempt at a Solution...

Homework Statement I don't have a homework question. I have more of a general question. Let's say we have a solution... x=C1*[a1 a2]^{T}*e^{lamda1*t} + C2*[b1 b2]^{T}*e^{lamda2*t} As t approaches infinity how do you determine what the solution does? Homework Equations...

Is there any software packages available to solve Differential equations(first order and second order)? This will be great help for me.

Homework Statement Suppose \alpha satisfies 1) a_{n} \alpha^{n} + .. + a_{0} = 0 Suppose that polynomial splits into n real linear factors ( it has n real roots ) Then, any solution of a_{n} y^{n} + .. + a_{1}y' + a_{0} = 0 is of the form y(x ) = c_{1}e^{\alpha_{1}x} + ...

Homework Statement The question is: Homework Equations I really don't know what to put here but my method is: -Find det(A-\lambdaI) -Find the roots of the determinant - which are the eigenvalues -Solve for (X -(\lambda)I) I am stuck at this part The Attempt at a Solution...

Hi there PF How does mathematicians usually prove differential equation (I am just speaking of the ordinary differential equations). We are going through proofs of differential equations in my high school math class at the moment, and in our books there are usual proofs, where one derives...

(I do not know how to make matricies with LateX, so where the semi-colon is denotes a new row!) t \vec{x'}=[-4,2;2,-1]\vec{x} The part that throws me off with this problem is the x' vector being multiplied by t! I know if the t wasn't there, all I would need to solve is det(A-(lamda)I)=0

y1(t) = t^(2)+5t, y2(t) = t^(2)-5t I know that these functions are linearly independent because they are not scalar multiples, but every time that i do the Wronskian i get 0. [t^(2) + 5t t^(2)-5t] [2t+5 2t -5] (2t^(3) -25t) - (2t^3-25t) = 0 my instructor some how...

A mass of 1 slug is suspended from a spring whose spring constant is 9lb/ft. The mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of square root 3 ft/s. Find the times at which the mass is heading downward at a velocity of 3 ft/s. I found...

Hey folks I'm looking for a way to find the characteristic equation for a second order coupled system of differential equations such as... \ddot{x} + A\dot{y} + Bx = 0 \ddot{y} + C\dot{x} + Dy = 0 Where x and y are functions of time. I know I can solve it by setting x and y to standard...

So basically I am a pure math major intending on going to graduate school to get a phd in some area of pure mathematics (possibly something like algebra or functional analysis), and I want to be well prepared for the more than likely outcome that I won't be able to obtain a permanent job in...

Homework Statement 1. Find the general solution to the differential equation: y''-5y'+6y = 0 Homework Equations The Attempt at a Solution m^2 - 5m + 6 = 0 (m-1)(m-5) = 0 y' = Ae^x+Be^5x

I just started learning about DE's and am impressed by how much information they contain. Are they usually just a relationship between several simpler functions? For instance, a basic kinematic problem like v = at + vo seems quite hard to come up with experimentally but v = d/t would be...

Homework Statement the full question is asking me to solve dy/dx + (1/x)y = 3cos2x i think i know what i am doing up to a point, but for me to continue with the question i have to integrate exp(x^-1)3cos2x and I am not sure how to do this, once i get this part i would know how to...

Hi. Anyway, learning this sort of makes me feel like I've chosen the wrong school for myself, but I'd like to try and see if I can understand this nevertheless. See, I'm supposed to learn various numerical methods for solving systems of linear equations, like the Jacobi or the Gauss-Seidel...

Homework Statement (2x*y-5)dx+(x^2+y^2)dy=0 test for exactness and solve Homework Equations The Attempt at a Solution I've been following an example to try and solve this but I'm not sure if its right or how to finish it of. \delta M/\delta y=2x \delta N/\delta x=2x...

Hello I am kinda confused when it comes to finding a general solution of equation. Here is the question. Y'' + 6Y' +9Y = 0 Solution Y'' + 6Y' +9Y = 0 I used "x" instead of Lamda...ANYWAY X^2 + 6X + 9 = 0 FACTOR IT WHICH IS (X+3) (X+3) = 0 X IS EQUAL TO -3. HERE IS WHERE I...

Homework Statement Q1) (dy/dx)= 2x(y2+9); y(0)=0 Q2) (x4+y2) dx - xy dy =0; y(2)=1 Q3) (dy/dt)= 4y+t Q4) y"+2y'+y=0; y(0)=4 and y'(0)=-6 Q5) y"+3y'+2y= 30e2t 3. Solutions found A1) y= tan (x2/3) A2) this is not an exact differential and so cannot be solved A3) couldn't solve this...

Studying a maths degree, going onto final year next year, am planning to do a 3rd year course in quantum mechanics. I just want to ask, how much probability theory and differential equations are there in quantum mechanics? Someone said that ultimately quantum mechanics is about probability...

Homework Statement ((d^2)x)/(d(t^2)) + 5(dx/dt) + 6x = f(t) f(t)=3 for (0<=t<6) f(t)=0 for t>=6 Homework Equations This I am not sure of, this is my question. Would I use the Second Order Differential equation to do this problem: L{((d^2)f)/(d(t^2))} = (s^2)F(s) - sf(0") -...

Homework Statement The pollutants are being added to the lake at a constant rate I, and the pollutants are thoroughly mixed into the lake. The annual precipitation into the lake matches evaporation, so the flow rate F is also constant. Let y(t) be the amount of pollutant in the lake and c(t)...

The rate of capital growth in a bank account is described by the differential equation dM/dt = aM Where dM/dt is the rate of change of the capital M and a is the annual interest rate. Show that the general solution for the time dependence of capital M(t) is given by: M(t) = M0 * e^at...

hi, first let me inform you that I'm not very good maths but love to learn it. I've basic understanding of maths. u take my maths abilities as 9th or 10th grader high schooler. i don't exactly know what linear algebra is but someone told me that it's about matrices. i have 4x4 and 6x6...

Homework Statement Given a system of differential equations and asked to find the equilibrium points and classify them. Homework Equations Equation 1 ... dx/dt=y(13-x^2-y^2 ) Equation 2 ... dy/dt=12-x(13-x^2-y^2 ) The Attempt at a Solution I know the solution...

Hi everyone, I recently started studying heat conduction using differential equations and this has been stumping me for a while. I am having trouble understanding what type of heat conduction problem this is. We are given a 100cm long copper rod with ends maintained at 0 C. The center of the...

I have a feeling this is the wrong place to post this. I can never figure out where to put things :confused: Anyway, my professor uses the 4th edition of Edwards and Penney Differential Equations and Boundary Value Problems (https://www.amazon.com/gp/product/0131561073/?tag=pfamazon01-20)...

Homework Statement \dot{x}=2x+5y+1, \dot{y}=-x+3y-4 Homework Equations The Attempt at a Solution Well, if system was: \dot{x}=2x+5y, \dot{y}=-x+3y we let a=2, b=5, c=-1, d=3. Then p = a + d and q =ad - bc and we investigate p^2-4q Don't know what to do when \dot{x}=2x+5y+1...

I am trying to solve a problem (not homework, too old for that! lol!) which involves the time dependent schrodinger equation for magnetic moment in time-dependent magnetic fields. I end up with the following that needs to be solved: x' = -i*(b*t-a*t^2)*x - i*c*y y' = -i*c*x -...

dy/dt = 2y-5, y(0) = y_0 The answer I got for this was y =5/2 + (y_0-5/2)e^t but the solution is y =5/2 + (y_0-5/2)e^-2t Where did this -2t come from? My steps: dy = (2y-5)dt Integrating both sides gives 1/2*ln|2y - 5| = t + C take exp of both sides gives 1/2(2y-5) = Cet...

Homework Statement Verify that each given function is a solution of the differential equation. 1. ty' - y = t^2 ; y = 3t + t^2 2. y'' + y = sect , 0<t<pi/2 ; y = (cost)ln( cost ) + tsint The Attempt at a Solution int (tdy) = int(t^2 + y)dt which isn't y=3t + t^2...

Homework Statement Consider a population p of field mice that grows at a rate proportional to the current population, so that dp/dt=rp. Find the rate constant r if the population doubles in 30 days. Find r if the population doubles in N days. Homework Equations ...The Attempt at a Solution...

Homework Statement 2(2x^2+y^2)dx-xydy=0 Homework Equations let x = yv dx = ydv+vdy The Attempt at a Solution (4v^2y^2+2y^2)(ydv+vdy)-vy^2dy=0 4v^2y^3dv+4v^3y^2dy+2y^3dv+2vy^2dy-vy^2dy=0 4v^2y^3dv+2y^3dv+4v^3y^2dy+vy^2dy=0 2y^3(2v^2+1)dv+y^2(4v^3+v)dy=0 dividing all sides by...

Homework Statement I have a series RLC circuit, no values given, connected to a voltage source Vs(t). I am asked to write the differential equations for: a. that relates the inductor current iL(t) to the source voltage Vs(t). b. that relates the capactor voltage Vc(t) to the source...

Homework Statement Greetings – I am wanting to solve the following system of differential equations: K*\frac{d^2x}{dt^2} = -K2*\frac{dz}{dt} K*\frac{dz^2}{dt^2} = K2*\frac{dx}{dt} Homework Equations The Attempt at a Solution Now – I am not just...

According to my school, I got to take calc 3 and 1 semester of linear algebra before i can start differential equations. Is this so? Anything else you would advise to add? Or is this too much and I can deal with less? I ask because many have advised calc 3 before any physics even though my...

Homework Statement The equation 2y'' - y' + y2(1 - y) = 0; where y' = dy/dx and y'' = d^2y/dx^2 represents a special case of an equation used as a model for nerve conduction, and describes the shape of a wave of electrical activity transmitted along a nerve fibre. Homework...

Thank you everyone for being a source of help in previous problems I've posted here. I'm starting an intermediate course in Differential Equations and I'm enjoying it so far, but this one problem on my homework seems to be giving me a problem and I think that I haven't fully grasped the...

Homework Statement Let M(x,y) = yf(xy) and N(x,y) = xg(xy), where f(v) and g(v) are functions of a single real variable v, defined and continuously differentiable for all real values of v. Under what conditions on f and g is the form Mdx + Ndy exact for all values of x, y in the plane? In that...

My professor has us using C. Henry Edwards and David E. Penney, Differential Equation and Boundary Value Problems, Fourth Edition. However, I don't really like it as our textbook. Anyone else have any recommendations?

Homework Statement I'm revising at the moment and a bit stumped on question 4 http://www.maths.ox.ac.uk/system/files/attachments/AC104.pdf Homework Equations The Attempt at a Solution I think for the first part of the question, the regular singular points are 0 and -2...

Homework Statement r" = 1/r^2 Homework Equations A friend gave this to me, he was just wondering how we'd approach it. The Attempt at a Solution I don't think the equation is linear, so I don't know how to approach it. My friend suggested integrating both sides with respect to r...

greetings, is it true that a exact differential equation is for two independent variable whereas linear differential equation is for one variable? advanced thanks,

Can anyone recommend an elementary but rigorous text on differential equations that takes care to distinguish between a function, f: X \rightarrow Y, and its value f(x) \in Y, as Spivak does in his Calculus. I find I'm getting rather confused by the traditional y=y(x) type dual-meaning notation.

Hi guys, I am trying to linearize a coupled non-linear ode. I used partial derivative, and then jacobian matrix, i have seen paper using state-space model of jacobian matrix. I can't get a proper reference on this state-space model. Attached is the non-linear ode, the partial derivative of the...