Differential equations Definition and 999 Threads

Homework Statement Determine the solution and limiting factor (t+1)y' + y = 6 y(1) = -2Homework Equations The Attempt at a Solution So I started off by isolating y' y' + y/(t+1) = 6(t+1) Then I found u(t) u(t) = e∫ t+1 dt = et2/2 +t y' =(et2/2 +t) = y(et2/2 +t) = 6(et2/2 +t)/(t+1)...

Homework Statement Use the method for Homogeneous Equations to slove (xy + y^2) dx - x^2 dy = 0 Homework Equations The Attempt at a Solution I attempted to get dx/dy on one side and substitute but could not get farther than this dx/dy = x^2/(xy + y^2)

Homework Statement I'm having problems with some differential equations, just need to know where I'm going wrong. Homework Equations The Attempt at a Solution a) mv\stackrel{dv}{dx}=F(x) mvdv=F(x)dx m∫vdv=∫F(x)dx v^2=vv^{2}_{0}+\stackrel{2}{m}∫F(x)dx...

Homework Statement Which of the following differential equations are linear? Put the linear differential equations in proper linear form a) t2dy/dt -et = ty b) dy/dt + ytan(t) -ety(2)=0 Essentially, I'm struggling with basic algebra. I've had no luck moving the dependent variable, y...

Author: Vladimir I. Arnold, R. Cooke (Translator) Title: Ordinary Differential Equations Amazon Link: https://www.amazon.com/dp/3540345639/?tag=pfamazon01-20 Prerequisities: Introductory Calculus Level: Adanced Undergraduate or Graduate Table of Contents: Basic Concepts Phase Spaces...

I am taking my first differential equations course. I am using the textbook by Edwards and Penney. My problem with this book is that it holds your hand a little bit too much. I don't like that I have to read huge amounts of explanation just to get a small amount of information. Does anyone know...

Homework Statement A falling body of mass m, encounters air resistance proportional to its instantaneous velocity, v. Use Newton's second law to find the DE for the velocity, v at time, t. Homework Equations I've been reading this section quite a bit and am still not getting it! I'd...

Author: David Bleecker (Author), George Csordas (Author) Title: Basic Partial Differential Equations Amazon Link: https://www.amazon.com/dp/1571460365/?tag=pfamazon01-20 Prerequisities: Table of Contents: Preface Review and Introduction A Review of Ordinary Differential Equations...

Homework Statement Solve: dP/dt + 2tP = P + 4t - 2 The Attempt at a Solution I've done a couple of these but I'm not sure how to start with this one... First I have to put it in standard form right? dP/dt + P(2t - 1) = 4t - 2 Then obtain the integrating factor by...

I am trying to figure out what I am doing. Forgive me, I’m not very sharp when it comes to differential equations… or even a useful working knowledge of calculus. I understand the concepts but if I can’t figure out how to type it into my TI-89 or get Wolfram alpha to do it… I’m kind of stuck and...

Homework Statement Show that sines and cosines are the solutions of the differential equation f''(x) = (-σ^2)f(x) What if a boundary condition is included that g(0) = 0? Homework Equations f''(x) = (-σ^2)f(x) The Attempt at a Solution Plugging in sin(σx) and cos(σx) yields an...

Homework Statement y = 2xy' + y(y')2; y2 = C1 (x + C1 /4) 2. The attempt at a solution I thought that I could take the first equation and set it equal to zero. But the C1 in the second equation is throwing me off. Am I supposed to set the second equal to C1?

Hi I am a physics major and I am trying to double major in math,I will be taking a differential equations course for pure math students this semester. I need advice on a good textbook in Differential Equations for pure mathematicians that will build up a great intuition for proofs and will have...

Can anyone explain why we obtain the part where i put the red underline. I understand everything until then

I'm having some difficulties figuring out how to linearize second order differential equations for a double pendulum. I have an equation that is in the form of \theta_{1}''\normalsize = function [\theta_{1},\theta_{2},\theta_{1}',\theta_{2}'] (The original equation is found at...

I'm only in a high school class. I just made up this problem to see if I'm getting the right idea in the long run. That, and then there's the fact that differential equations are SO MUCH FUN! :biggrin: Homework Statement Molecular bromine (initial concentration: 0.49 M) and formic acid (initial...

(d4x)/(dt4) + (1/(1+t))*(d2)/(dt2) = x(t) Is this differential equation linear or non-linear? I don't understand the difference.

Homework Statement http://sphotos-d.ak.fbcdn.net/hphotos-ak-ash3/526007_3920535257917_1525052730_n.jpg Write down the differential equations of motion. (Step by step if you can)2. The attempt at a solution x"+(f/m)x'+3(k/m)x=0 or x"+σx'+ω^2x=0 where σ=f/m and ω=sqrt(3k/m) Thanks in advance.

Can anyone recommend a good differential equations and linear algebra book? The books that I've read so far are Linear algebra: https://www.amazon.com/dp/0030103479/?tag=pfamazon01-20 Differential Equations: https://www.amazon.com/dp/0534373887/?tag=pfamazon01-20 I was able to get an...

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?