Differential equations Definition and 999 Threads

Homework Statement Solve this system of differential equations \begin{equation} x'_1=5x_1 + 2 x_2 - x_3 \\ x'_2=-2x_1 + x_2 - 2x_3 \\ x'_3=-6x_1 - 6 x_2 \end{equation} Homework Equations The Attempt at a Solution This is my first time solving a problem like this and I just...

Homework Statement How do you derive the time-dependent velocity equation for motion along a curve, such as a skateboarder on a half pipe? For the sake of abstraction, I ask myself the following: A uniform sphere of mass m and radius r is set free from the top edge of a semicircle half pipe...

Homework Statement Here is the question along with my work. I attempted to solve for the actual solution using both eigenvectors. From what I have been taught it should yield the same answer... But as you can see (circled in red) the solutions are clearly different. Is this normal or maybe...

Hi guys, in my college we have this "Independent Study" component for the Intro Linear Algebra class. Basically, I have to solve 4 questions that go beyond what was covered in class. Sadly, being the procrastinator I am, I haven't looked at it until now and the assignment is due Friday. The...

Hi. I just came back from my differential equation midterm and was surprised to see a problem with the Riemann-zeta equations on it. I think the problem went something like "Prove that \pi/6 = 1 + (1/2)^2 + (1/3)^2 + ... " The study guide did mention that "prepare for a problem or two...

Hi, I searched the forums but was unable to find any thread about DE textbooks so I'll start one. I'm looking for a good DE textbook, mostly focusing on ODEs, something comprehensive and complete and not too old fashioned. Does anybody have any recommendations? Thanks.

Homework Statement tx'' + (4t-2)x' + (13t-4)x = 0 Use laplace transform to solve. The Attempt at a Solution I've split up the X'(s) and X(s) and integrated to get X(s) = \frac{c}{(s^2 + 4s + 13)^2} = \frac{c}{9} \left[ \frac{3}{(s+2)^2 + 9} \right]^2 From this I'm guessing...

Homework Statement Determine all fixed points of: dx/dt = x(β-x-ay) dy/dt = y(-1+ax-y) β and a are parameters. I get what to do when there is just one differential equation, but not two.

Homework Statement Two same aged people P1,P2 create bank accounts at ages 25,35 respectively, and add 2000 euros annualy , for 10,30 years respectively. No initial capital in the accounts. 1.For interest 8% , what's the balance of each acount at age of 65 of P1,P2? 2.What should be the...

"Ordinary Differential Equations" by V Arnold Hello, I recently bought "Ordinary Differential Equations" by V I Arnold to study differential equation. In that book he assumes we know basic topology. I want to know which subfield of topology should I know, in order to study this book...

Differential equations Homogeneous Linear Equations case 1 +example - YouTube There are more on my channel and will be posting more daily.

I'm a bit confused on how to do this problem, here is what I have. Part a) I must set up the set of linear differential equations with the initial values. Using the balance law gives y0'=0.2+0.1-0.2-0.1=0 The other 2 net rate of change would be equal to 0 as well. But...I don't think I did...

Why is it that the unilateral lateral Laplace transform is used when given initial conditions that are non-zero. Is there a reason that explains why it would be wrong to use the bilateral Laplace transform instead? I know bilateral does not have any input of initial conditions but that does not...

Just curious if anyone has any good recommendations for books or resources on Linear Partial Differential Equations. Thanks.

Homework Statement I have to solve the differential equation xy'' + y' + xy = 0 ; x_o = 0 Homework Equations The Attempt at a Solution I know that a solution is y= sum from 0 to infinity (an (x-1)^n) I then differentiate it twice to get y' = sum from 1 to inifinity...

Hello, I'm a mechanical engineering student working on my senior design project. It involves the automated correction of an electrolyte's chemistry. That being the pH, conductance, and zinc concentration. One of the tasks is to apply a "transient control analysis". This involves creating...

Homework Statement (Sorry, I don't know how to use latex) Solve the TDSE for a spin half nucleus in a B-field where B_z = B0, B_y= B1 cos(ωt) and B_x = B1 sin(ωt). Use vector and matrix representation. You will get coupled differential equations for a and b, look for solutions of the form a =...

Homework Statement Show that Acos(ωt) + Bsin(ωt) can be written in the form r*sin(ωt - θ). Determine r and θ in terms of A and B. If Rcos(ωt - ε) = r*sin(ωt - θ), deermine the relationship among R, r, ε and θ. Homework Equations Trig identities. The Attempt at a Solution I'm...

I'm a math major, which means I genuinely like mathematics. But I may be becoming a "pure math snob:" http://img.spikedmath.com/comics/446-pure-math-vs-applied-math.png When I'm working on differential equations, I'm finding it very tedious, like it's "not my kind of math." My brain...

Hi everyone! :smile: I'm newbie in this forum, please help me for my question. In differential equation we know that the differential equation has a solution and uniqueness. which is usually called the existence and uniqueness theorem. my question, what is the difference of local existence...

Homework Statement The Attempt at a Solution I tried two different methods and came to an odd conclusion:

Homework Statement When solving a D.E. with power series, I've encountered something along the lines of: (2 - r)^{2}g'' = -2 Homework Equations Power Series The Attempt at a Solution I know I am just supposed to assume such a series exists, and work from there. But I'm really...

Homework Statement The value of a tract of timber is ## V(t)=100,000 e^{0.8\sqrt{t} } ## where t is the time in years, with t=0 corresponding to 1998. If money earns interests continuously at 10%, the present value of the timber at any time t is ## A(t)= V(t)e^{-.10 t} ## Find the year in...

Hi there guys. Homework Statement I am trying to solve a circuit that has a constant voltage source (V) in series with an inductor (L), then that inductor is connected to a resistor (R) in parallel with a capacitor (C). Homework Equations ------- The Attempt at a Solution...

Hello, I have recently started a little implicit differentiation and I have seen DEs before but I know that I still need to work on my differentiation and integration a little more before I am ready to tackle those. Anyway, I wish to ask, what distinguishes implicit differentiation from a...

Homework Statement A goose starts in flight a miles due east of its nest. Assume that the goose maintains constant flight speed (relative to the air) so that it is always flying directly toward its nest. The wind is blowing due north at w miles per hour. Figure 8 shows a coordinate frame with...

There are two questions that I am trying to solve on web assignment. The goal is to find a general form of a particular solution to each ODE. The question asks me to represent all constants in the solution using "P,Q,R,S,T..etc.", in that order. 1. y'''-9y''+14y'=x2 2. y''-9y'+14y=x2e4x...

Hey Everybody, I am supposed to model the trajectory of a golf ball. I have been given the equations for velocity as a function of its derivative with respect to time. I am supposed to find the x-range as a function of the angle θ. (Pardon my bad latex skills, I will fix mistakes)...

dε/dt=d(uε)/dZ+[(e^(-k1t) - e^(-k2t)] where ε=% area opening, u= velocity, Z=length , k1, k2= constants, t= time Please help me how to solve the ODE

Homework Statement Suppose a rocket is launched from the surface of the Earth with initial velocity v_0 = \sqrt(2gR) , the escape velocity. a) Find an expression for the velocity in terms of the distance x from the surface of the Earth (ignore air resistance) b) Find the time...

find a solution of (a^2-x^2)y''-2xy'+n(n+1)y=0, a not 0 by reduction to the legendre equation?

I'm taking my first ODE course, and I'm unsure what is meant in this question when it asks "Solve the following differential equation" (I have a list of DEs to solve). Some of them are really messy and I can't figure out an implicit solution. Would an explicit solution be acceptable? Example...

Homework Statement I came across two, not so obvious DEs that have stumped me abit. (1) x2y' = xy + x2ey/x (2) x2y' + 2xy = 5y3 Homework Equations I know these are not separable, and more than likely require an integrating factor to put them into exact form so I can integrate them...

Hello all~ Given the equation: dy/dx = (x/y) I know we would initially go to: ∫dy =∫ (x/y) dx then too: ∫(y)(dy) = ∫x dx Until arriving at: (y2/2) + C1 = (x2/2) + C2 (y2) - (x2) = C My question is: Where does the dy disappear to in step 4? Where the anti-derivative is taken...

HOW IS THE FOLLOWING QUESTION DONE? Milk chocolate is being produced in a 300 litre tank, which initially contains 100 litres of milk. The following things then occur simultaneously:  1. Liquid cocoa (made up of equal parts cocoa solids and cocoa butter, both in liquid form) is added at...

Consider the equation dy/dt = alpha - y^2 a) Find all of the critical points. How does it change as alpha < 0, alpha = 0 or alpha > 0? b) In each case of different alphas, consider the graph of f(y) vs y and determine whether each critical point is asympototically stable, semistable, or...

I am working on some problems for an assignment in my PDEs class and find myself either not understanding what I am supposed to do or being unsure of my answers or the next step. I am going to outline my understanding of the problems, provide my attempt at a solution and highlight where I am...

I am trying to solve and plot the differential equations for springs. when the damping factors are under 1 (underdamping), I tried damping ratios of: 0.01, 0.2, 0.1, 0.4, 0.8 If I use the following equations (wd= damped frequency, wn= natural frequency, v0= v initial, x0= x initial, t=...

Homework Statement (x+2y+3)dx+(2x+4y-1)dy=0 a1= 1 b1=2 a2=2 b2=4 a2/a1=b2/b1 Therefore z=x+2y Here is where I get confused I understand that they must get a dz in the equations thus they take the derivative with respect to y of the following equation z=x+2y thus giving dz=dx+2 or...

Homework Statement dr/d∅+rtan∅=cos∅ μ(∅)=exp[∫tan∅] μ∅=exp[-ln[cos∅]=-cos∅ -cos∅(dr/d∅)-rtan∅cos∅=-cos^2∅ dr/d∅[-rcos∅]=-cos^2∅ rcos∅=∫cos^2∅ changed cos^2∅ to 1/2+1/2cos2∅ rcos∅=1/2∅ + 1/4 sin2∅+c the books answer is not even close to mine they have r=(∅+c)cos∅...

Homework Statement Match each of the differential equations with a solution from the list below. 1. 2x^2 * y'' + 3xy' = y 2. y'' + 12y' + 36y = 0 3. y'' - 12y' + 36y = 0 4. y'' + y = 0 And then the possible solutions A-D Homework Equations The Attempt at a Solution This is...

Unfortunately I am unable to fit a first course in differential equations into my schedule, therefore I have opted to self study the said course. I am looking for a textbook appropriate for an introduction into differential equations that isn't too ambiguous to tackle on my own. I am an EE major...

Homework Statement (y+2)dx +y(x+4)dy=0 Homework Equations The Attempt at a Solution ∫(1/x+4)dx + ∫(y/y+2)dy=0 ln(x+4)-2ln(y+2)+y=lnc Here is where I get confused how do I make this into an explicit solution, that +y really bothers me. I was thinking ln [...

Homework Statement Tan∅ dr + 2r d∅=0 Homework Equations The Attempt at a Solution ∫1/2r dr +∫1/tan∅ d∅=0 1/2ln(2r)+ln(tan∅)=c ln[r(tan∅)]=ln(c) r(tan∅)=c the solution in the book says the answer is rsin^2∅=c Where did I go wrong? Thank you

Homework Statement Solve y''=1+(y')2 in two ways, for x is missing and y is missing. Homework Equations Integration, and reduction of order. The Attempt at a Solution First method: (this is correct) y''=1+(y')2 let y'=p and y''=p' p'=1+p2 p'/(1+p2)=1 ∫p'/(1+p2)dx=∫1dx arctan(p)=x+c solve...

Homework Statement (x2+2y')y''+2xy'=0 with initial conditions of y(0)=1 and y'(0)=0 Homework Equations reduction of order, and exact equations.. The Attempt at a Solution let y'=p and y''=p' Giving: (x2+2p)p'+2xp Let M=2xp and N=(x2+2p) So, Mp=2x and Nx=2x Therefore, they are...

Hi all, I have a homework assignment related to the conservation of energy in a fluid. This is given in terms of the density ρ, specific heat c_{p}, thermal conductivity k, bulk viscosity μ, dissipation function \widetilde{\phi}_{v}, velocity function \widetilde{u}, spatial derivative of the...

Homework Statement uploaded file (Problem 5)Homework Equations uploaded fileThe Attempt at a Solution Ok so I think I have the correct answer but the problem is I don't know how to solve for the actual answer with 2 equations which one do I plug into? Sorry for all the erasing!

Homework Statement What function do you know from calculus is such that its first derivative is a constant multiple k of itself? (Do not use the function f(x) = 0.) Homework Equations The previous question asked what function was a derivative of itself - with the pretty easy answer...

Hello everyone, I am making use of Mathematica to solve differential equations developed by Lagrange method, I have met some problems in solving the equations, I cannot obtain the correct result even though I have set "t" and "MaxSteps" both as "Infinity". I have run the program for 7...