Differential equations Definition and 999 Threads

i am told to investagate the nature of the critical points of the system: x'=e^y y'=(e^y)*cos(x) i am not sure where to begin because x' is always non-zero.

Need Help with a couple diff eq problems: 2.) show y=cx^2 - x is a solution of xy' - 2y + x =0 I was trying to separate the variables so i could integrate but i cannot get it to work out. I have tried so many things from adding 2y to both sides and and multiply by the inverse dx/dy. but...

Homework Statement Consider the implicit (not actually sure wether that's the correct english word, my material is in Finnish and I'm Swedish-speaking :smile:) method xj+1=xj+h/2(f(tj,xj)+f(tj+h,xj+1)) a)Write an appropriate Runge-Kutta scheme b) What is the methods rank when we use the...

1. Suppose we have two tanks, each with an inflow pipe and an outflow pipe and also connected to each other by pipes. At the start, tank A contains 40 gallons of clean water and Tank B contains 25 gallons of clean water. At t = 0 brine containing 0.5 lbs of salt per gallon begins to flow into...

What is the difference between the behavior of solutions that are exact and those that are not?

Homework Statement solve the system of first-order linear differential equations: (y1)' = (y1) - 4(y2) (y2)' = 2(y2) using the equation: (λI -A)x = 0 Homework Equations using eigenvectors and eigenvalues in the book 'Elementary Linear Algebra' by Larson and Falvo - Section 7.4 #19...

Hey.. I ran across some problems and the notation used is a little different from what I've seen before. considering U(x,y)=X(x)Y(y) Sometimes I'll see Uxx for \frac{d^{2}u}{dt^{2}} which equals X''Y Or Ux for \frac{du}{dt} which equals X'Y But what about U'x Is that a redundant way of...

Homework Statement Given that y1(t) = t is a solution of t2y'' + ty' - y= 0 find all solutions. The Attempt at a Solution I already put it into mathbin asking somewhere else for help and it doesn't look like i can copy paste that syntax to here. http://mathbin.net/56336 Could...

I want to preface this by saying that these questions are not to find an exact answer, just to build intuition. If you find them ill-posed or incorrect, it would be most helpful if you could show me a "better way" of looking at it. So, I'm trying to gather a geometric viewpoint of...

Homework Statement Let K = \{ (x,y) | -1<x<1 , -1<y<1 \} . Find the unique soloution of dirichlet problem: \Delta u(x,y) =0 , (x,y) \in K , u(x,y) = |x+y| , (x,y) \in \partial K . Homework Equations The Attempt at a Solution We need to guess a soloution and not use...

Homework Statement y'' + 2y' +y = 5e^6x use undetermined coefficients to solve this equation. Homework Equations The Attempt at a Solution what I would normally do is m^2 + 2m + 1 = 0 but then I get stuck I can't find the general equation as this won't factor. I tried...

Homework Statement dx/dy = cos(y) - xtan(y) I need to find the general solution of the problem Homework Equations y' + Py = Q Where P and Q are functions of x dy/y = - Pdx ln(y) = -integral(Pdx)+c y = e^(-int(Pdx)+c) The Attempt at a Solution Now I have no idea...

Homework Statement [b]2. Homework Equations [/bHomework Statement I have to find a(t) and b(t), using the following set of equations: \frac{\hbar\omega_{1}}{2}a(t)\cos{\alpha}+\frac{\hbar\omega_{1}}{2}b(t) exp(-i\omega t) \sin{\alpha}=i\hbar\frac{da}{dt} \frac{\hbar\omega_{1}}{2}a(t)...

Homework Statement ax^{2}\frac{d^{2}y}{dx^{2}}+bx\frac{dy}{dx}+cy=0 Let x= e^{t} Find \frac{dy}{dx} and \frac{d^{2}y}{dx^{2}} in terms of \frac{dy}{dt} and \frac{d^{2}y}{dt^{2}} The Attempt at a Solution if x= e^{t} then \frac{dx}{dt} = e^{t}= x \frac{dy}{dx}= \frac{dy}{dt}\frac{dt}{dx}=...

I have been trying to solve a problem MATLAb regarding my project and it involves solving set of differential equations involving four variables. It is turning into quite a headache and i was actually wondering if ode45 or ode23 would be sufficient for such a problem. Problem Structure...

Homework Statement solve the system: dx/dt = [1 -4] x _______[4 -7] with x(0) = [3] __________[2] Homework Equations The Attempt at a Solution I got both eigenvalues of the matrix are -3 and so both eigenvectors are [1]...

Homework Statement A ladder, of length 13m, is leaning against a wall. The base of the ladder begins to slide, frictionless, away from the wall; by the time the base is horizontally 12m away from the wall it is moving at a rate of 2ms-1 a)How fast is the top of the ladder sliding down the...

Hello guys, I am new here to the forum and I was wondering if you could help me with some trouble I am having with differential equations. For your information: I am a second year applied physics student from the Netherlands and I loveee everything about physics and mathematics! The problem...

Ok, I've been working this one out for a while, and I just can't seem to get it. I'm looking for the condition such that x(t)=k (where in our class, K generally equals e^c) The initial equation is as such: 7t^2(dx/dt)+3x+5=0 I've worked the equation down to two different forms: x...

1. L-1{(3s+2)/ (s2+2s +10)} After completing the square I get to 3s+2 /(s+1)2 + 32 which suggests two solutions or one. They decompose the fraction into [(A)s+1 /(s+1)2 + 32 ]+ [(B) 3/(s+1)2 + 32] I am unsure of how this decomposition works I thought that we would take A(3s) as the numerator...

Last night in a lecture my professor explained that some partial differential equations are used to observe events on minimal surface (e.g. membranes). A former advisor, someone that studied differential geometry, gave a brief summary of minimal surfaces but in a diffy G perspective. 1.)...

Homework Statement Find a particular solution of y'' + 2y' + 5y = e^x * sin(x)Homework Equations The Attempt at a Solution Characteristic equation: r^2 + 2r + 5 = 0. Through quadratic formula, r1 = -1+2i and r2 = -1-2i, so my homogeneous equation is y_h = c1 * e^(-x) cos(2x) + c2 * e^(-x) *...

Homework Statement Find a particular solution using variation of parameters. y'' + 3y' + 2y = 4e^x Homework Equations yp = -y1 * INT (y2f(x)/W[y1,y2]) dx + y2 * INT (y1f(x)/W[y1,y2]) dx The Attempt at a Solution So, first I find the homogeneous solution, correct? r2 + 3r + 2 = 0, so...

Homework Statement I'm told to solve the following: X' = (1 1; -1 3)X Where (1 1) is the first row and (-1 3) is the second row. The Attempt at a Solution Okay so I calculated teh eigenvalues and I got repeated eigenvalue of 2. I calculated the eigenvector and got (1,1). So a solution...

Homework Statement trying to find the integral curve for ths equation get stuck at trying to integrate 10^-u dy/dx=10^x+yHomework Equations The Attempt at a Solution let u=x+y so dy/dx=10^u du/dx=1+dy/dx =(10^u)-1=du/dx du/dx=(10^u)-1 du/10^u=-dxthanks in advance

Solve: dx/dt=3-x initial condition x(1)=4.

Homework Statement What do you do if one of the roots to the characteristic equation of a differential equation is zero when using variation of parameters? Homework Equations The Attempt at a Solution The problem I encountered this in is y" - y' = 4t Characteristic equation r2 - r = 0 so...

Homework Statement Solve the following: xdx = y^{2}dy Homework Equations Fundamental theorem of calculus - thanks gabbagabbaheyThe Attempt at a Solution \frac{dy}{dx}=\frac{x}{y^{2}} \int\frac{dy}{dx} = \int\frac{x}{y^{2}} =\frac{x^{2}}{2y^{2}} So with the question, I've integrated both...

Critical Points and Differential Equations! Helppp Hello everyone..Find it embarrassing enough on asking a question on my very first post but I've been an avid reader of the forums for the past couple of months and been finding what i need for all my assignments here.So a big Thank You to all...

I am a Matlab rookie. I need to solve numerically the following second order differential equations d^2x/dt^2 + w0_(el) * x = e/m_e * E - K3/m_e * x *y; d^2y/dt^2 + w0_(v) * y = - K_3/2M * x^2; I have started to deal with only the harmonic part of the problem. So I tried to solve...

http://img19.imageshack.us/img19/9946/matlabhelp.png Alright guys, I am extremely new with MATLAB, and this ODE problem is giving me a hard time. For my function file, I got function dy = hode(t,y) dy = [y(4); -(3/5)*y(4)-(138/100)*y(3)-(231/500)*y(2)-(2929/10000)*y(1)]; end...

Homework Statement i had solve the C1 question, But in c2, i am not sure what is the relationship between r(t)=x^2(t)+y^2(t) and the r'=r-r^3. not get the meaning of that question, how to use the r(t)=x^2(t)+y^2(t) to get the r'=r-r^3? can anyone explain to me? thanks!

Homework Statement Consider the initial value problem: x'' + 2x' + 5x = δ(t - 1); with: x(0) = 0 and x'(0) = 0. Using Laplace transforms, solve the initial value problem for x(t). Homework Equations L[x''] = (s^2)*L[x] - s*x(0) - x'(0) L[x'] = s*L[x] - x(0) L[δ(t - 1)] = e^(-s)...

An integrating factor e^(integral p(x) ) can be used to solve Linear D.E. in form y' + P(x)y=Q(x), but what do i do when there is no x in P(x) or Q(x)? for instance in these problems: #1)y' - y=4(e^x) #2)y'+2xy=4 Is it wrong to use P(x)= -1 for problem 1, and Q(x)=4 for problem 2? This...

Homework Statement Consider the following model for the populations of rabbits and wolves (where R is the population of rabbits and W is the population of wolves). dR/dt = .05R(1-.00025R)-.00109375RW dW/dt = -.04W+8e-05RW Find all the equilibrium solutions: In the absence of...

riccati differential equations -------------------------------------------------------------------------------- how to find general solution of this question du/dt=u^2+t^2 please say me i work hard but i do nat know this form of riccati equation. i know when special solution is...

When given y'' + ay' + by + c = 0 The characteristic equation is: λ^2 + aλ + b = 0 Now I'm making a substitution of e^(λx) to get [(λ^2 + aλ + b)][e^(λx)] = 0 double root : [(λ - alpha)^2] [e^(λx)] = 0 My question now is that if I were to do the same thing with the...

Homework Statement y''+7y'=392sin(7t)+686cos(7t) with y(0)=4 and y'(0)=9 Homework Equations No real relevant equations The Attempt at a Solution I assumed since the g(t) has function of both sine and cosine the solution would be both the real and non real parts of the solution to...

Homework Statement Let Ly = y'' + py' + qy. Suppose y1 and y2 are functions such that Ly1 = f(x) and Ly2 = g(x). Show that the sum y = y1 + y2 satisfies the nonhomogeneous equation Ly = f(x) + g(x). Homework Equations Superposition Principle: L[c1y1 + c2y2] = c1L[y1] + c2L[y2] The...

Homework Statement I have a Driven Harmonic Oscillator Without a Damping Force Homework Equations m\ddot{}x+kx=F0 cos(\omegat)The Attempt at a Solution Not looking for a solution just looking for an example problem, as none are provided in my text. If anyone can provide one for me I'd be very...

I could not get LaTex to format properly, so I typed out the question and my work using Microsoft Word's equation editor. Please see the attached document, apologies for any inconvenience! These problems involve the techniques for the method of undetermined coefficients and variation of parameters.

Homework Statement Solve the differential equation with the initial condition y(0) = 1 Homework Equations 3e5xdy/dx = -25x/y2 The Attempt at a Solution First I tried putting everything with an x or dx on one side and a y or dy on the other side, and solved for C. I got 0 as the...

Homework Statement see attached Homework Equations The Attempt at a Solution Question 7a) I can do but 7b I am not sure how to start. I think x with a dot means differential with respect to time? need some help starting. Thanks

Homework Statement Let f(t) be the solution to the initial value problem 2t(dy/dt)+y=t^4 with f(0) = 0 find f(t). Homework Equations The Attempt at a Solution I tried to do this by separating variables but that hasn't gotten me very far. I don't know if I can do it by doing...

Homework Statement \frac{dx}{dt} +\frac{dy}{dt} + y - x = e^{2t} \frac{d^2x}{dt^2} +\frac{dy}{dt} = 3e^{2t} I am a little stumped on this one. I tried writing it using D as the differential operator d/dt: D(x+y) +x - y = e2t D2x+Dy = 3e2t but that doesn't do anything but...

Hello, I joined a class on Partial Differential Equations 3 or 4 lectures late, so I have missed the classes outlining how to solve the simplest forms of them. I am trying to understand the textbook, but so far it is not going so well for me, so I just need to ask some questions about the...

Homework Statement So my friend asked me for help because he assumed having a math degree meant I knew math :rolleyes: [PLAIN]http://courses.webwork.maa.org:8080/wwtmp/equations/0e/c5a05957810916cfdff379ee0642fc1.png (dx/dt=−4y and dy/dt = −4x) Convert this system to a second...

If we have differential variable of matrix kind ( with dimention 3*3 ) and non matrix ( with dimention 1) simaltanously and as a couple ,how can we use ode45 ? If we have only matrix kind , we can use m file of ode at first with the command of reshape (3,3) and then change it to column one.What...

can anyone help me to solve this equation ?. is this equation linear or not? knowing, this equation represents the equation of motion for frame members for materials which have different moduli in tension and compression (civil engineering). "EI" ("x,t" ) ("∂" ^"4" "u" ("x,t" ))/〖"∂x" 〗^"4"...