Differential equations Definition and 999 Threads

Homework Statement This is the first problem of the two. Homework Equations The Attempt at a Solution Using separation of variables, I end up with T'(t)= -λKT(t) and X''(x)+(β/K)X'(x)/X(x)= -λ. At first I chose the negative lambda because I saw that U(0,t) and U(L,t) needed to oscillate...

Homework Statement Verify that the indicated funciton is a solution of the given Differential Equation. c1 and c2 denote constants where appropriate. \frac { dX }{ dt } =(2-x)(1-x);\quad \quad \ln { \frac { 2-x }{ 1-x } } =tThe Attempt at a Solution I'm not quite sure how to really start...

Homework Statement Find a particular solution Yp of the given equation. Primes denote deriviate with respect to x (method of flexible guess) Homework Equations 4y''+4y'+y=3xe^x The Attempt at a Solution when I used y=Ae^x as guess my A depended on x So y=Axe^x gave me 12A+9Ax=3x...

Homework Statement When you turn on an electric heater, such as "burner" on a stove, its temperature increases rapidly at first, then more slowly, and finally approaches a constant high temperature. As the burner warms up, heat supplied by the electricity goes to two places. i.) Storage in...

Homework Statement A biologist prepares a culture. After 1 day of growth the biologist counts 1000 cells. After 2 days he counts 3000. Assuming a Malthusian model what is the reproduction rate and how many cells were present initially. Homework Equations P(t) = Ce^{rt} The...

Homework Statement http://img192.imageshack.us/img192/6482/asderl.jpg Find S(t). Homework Equations I managed to find these equations, but don't know how to solve them completely. mx``=Rsinφ my``=Rcosφ-mg xtgφ+y=h x`(0)=0; x(0)=0; y`(0)=0; y(0)=hThe Attempt at a Solution Need to find...

Dear MHB members, Suppose that $p,f$ are locally essentially bounded Lebesgue measurable functions and consider the differential equation $x'(t)=p(t)x(t)+f(t)$ almost for all $t\geq t_{0}$, and $x(t_{0})=x_{0}$. By a solution of this equation, we mean a function $x$, which is absolutely...

Homework Statement For the system of differential equations \frac{dx}{dt}=(-3x-y) \frac{dy}{dt}=(-2x-2y) (a) Find the general solution. (b) Find the solution if x(0)=1 and y(0)=2. Homework Equations The Attempt at a Solution I have absolutely no clue how to do this. I have never seen a...

I'm having trouble understanding what uniqueness is/means. When given a slope/direction field I don't know what I should be looking for if asked to determine if a given initial condition has a unique solution. Example: \textit{y' = }\frac{(x - 1)}{y} With this equation I can see that as long...

i'm stuck on three problems on my homework - I've been trying to solve them forever! please help? thanks in advance. PS I'm new on here and don't know what to do so I'm just going to type out the problems haha 1) Evaluate: integral of the absolute value of x^2-9 dx on interval [-4, 6] 2)...

Hi all, Back on MHF, my Differential Equations Tutorial was beneficial to many members and I was proud of my contribution to the site. However, with the fall of MHF, I have not been able to retrieve my old posts. So my plan is to start a completely new one on this site -- from scratch. I...

I am currently taking differential equations in college but I am having trouble understanding a few things. Our teacher is from Russia so it makes it a bit harder for me to understand him and sometimes for him to understand our questions... Currently I have taken Calc 1, 2, 3 and Linear...

Homework Statement Solve the differential equation dy/dx = 3x2(1+y2)3/2 Homework Equations The Attempt at a Solution So far this is what I have (I'm almost finished) - ∫dy/(1+y)3/2 = ∫3x2 dx Let y = tan(u) , dy = sec2(u) Then (1+y2)3/2 = (tan2(u)+1)3/2 = sec3(u) and u =...

Homework Statement Utt-Uxx+2Uxy-Uyy=0 with the conditions: U(1,x,y)=cos(x)+ey Ut(1,x,y)=sin(x)-y2 Homework Equations Not using separation of variables to solve. The Attempt at a Solution I've gotten the general equation to be of the form: U(t,x,y)=ψ(x+t,y-t)+ζ(x-t,y+t)...

Before taking Differential Equations/Linear Algebra in my first year of college, I am brushing up on Algebra I/II, Pre-Calculus, and Calculus I/II. Should I also run through Trigonometry as well or should I not waste my time on it if I don't have enough time to go through everything else first...

Homework Statement Solve x^2\frac{du}{dx} = 0 in the sense of distributions. Homework Equations <u',f> = -<u,f'> for any test function f. The Attempt at a Solution My thinking is that since we want to see the action of the left hand side on a general test function f, we try...

(dy/dx)^2 + y^2 + 4 = 0; Show that there are no real valued solutions. (dy/dx)^2 = -(y^2 + 4) dy/dx= sqrt( -(y^2 + 4)) -----> This is the answer I got, I feel it makes sense because the negative under the radical produce an answer with 'i' or an imaginary sol'n and since y^2 is always...

Homework Statement 1. For the system of equations x'(t) = 4y and y'(t) = x, obtain the equation of the trajectory (path in the phase plane) that passes through (2, 0). For this trajectory, what is the equation of the slant asymptote that (x(t), y(t)) approaches as t goes to infinity? 2...

Homework Statement Vibration in a system can be a source of problems. For example, the deck on a ship could vibrate due to the engine which represents a forcing function. This system may be simply modeled by a mass, representing the deck, a spring representing the stiffness of the deck and a...

Are you a software engineer using differential equations or more advanced math everyday to solve problems? I would like to hear about what you do--what projects do you work on? Do you consider that differential equations and advanced math skills are useful/in demand in the realm of software...

Ok guys, I've got an issue with a coupled differential equation and I just can't get to solve it: \frac{\partial r}{\partial t} = Q\frac{\partial c}{\partial t} Obviously, r depends on c and visa versa, but they both depend on time. Is there a way to uncouple these variables and solve the...

I’m reviewing differential equations after taking the course about 5-6 years ago and I have a couple of questions about the solutions of differential equations. 1) First why is the general form of the solution to linear homogenous differential equations, with non-equal and real roots to the...

can you help me ?? A 200 liter tank initially contains 100 liters of water with a salt concentration of 0.1 grams per liter. Water with a salt concentration of 0.5 grams per liter flows into the tank at a rate of 20 liters per minute. Assume that the fluid is mixed instantaneously and that...

Homework Statement dy/dt=y((3t^2)-1), y(1)=-2 Homework Equations Basic integrals The Attempt at a Solution integrate on both sides: dy/y=dt((3t^2)-1) ========>ln(y)=(t^3)-t+c ========>y=e^((t^3)-t+c) ========>y=e^((t^3)-t)e^(c) I am not sure if its some e rule that I forgot...

Homework Statement Consider the following system of (first order) differential equations: \dot{x}=f(t_1,x,y,z) \dot{y}=g(t_2,x,y,z) \dot{z}=h(t_3,x,y,z) where \dot{x}=\frac{\partial x}{\partial t_1}, \dot{y}=\frac{\partial y}{\partial t_2}, and \dot{z}=\frac{\partial z}{\partial...

Hi everyone, I'm not quite sure how to proceed to show existence (and perhaps uniqueness) of the following system of (first order) differential equations: \dot{x}=f(t_1,x,y,z) \dot{y}=g(t_2,x,y,z) \dot{z}=h(t_3,x,y,z) where \dot{x}=\frac{\partial x}{\partial t_1}...

Hi guys, I'm currently in computer science program and I have an urgent feeling that I need better exposure to math. I have taken Discrete Math, Calculus i, ii, iii and I've independently studied linear algebra. I guess my concern is lack of differential equations and numerical methods. In...

The Wikipedia article regarding Lagrangian Mechanics mentions that we can essentially derive a new set of equations of motion, thought albeit non-linear ODEs, using Lagrangian Mechanics. My question is: how difficult is it usually to solve these non-linear ODEs? What are the usual numerical...

I curiously never had a problem solving Seperable Equations in the Seperable Equations chapter of the Boyce/Diprima book. I am the kind of person who likes to do things the long way, and encountered a problem solving for an Integrating Factor(Linear ODE, NOT EXACT) the long proofy way. I tend...

Homework Statement In control engineering, I want to have a mathematical model of a physical system as a set of input, output and state variables related by higher order differential equations. 2. Relevant concepts As we all know that, in control engineering, we can solve linear-system...

Homework Statement I'm given two equations for coordinates of a certain particle in the xy plane, \dot{x}+ωy=0 and \dot{y}-ωx=0. Then using the complex variable z=x+iy, find the differential for z, and solve it. Hence give x and y as functions of time. Homework Equations The...

Hello all, Next semester I will be taking a Network Analysis course in my EE degree. Moreover, we will be utilizing numerous mathematical concepts I have not yet seen. If anyone has (preferably free) access to any of the concepts to follow that they would be willing to share, I would be...

At my school, Physics majors are the only ones who HAVE to take PDE, math majors and engineers have the option as an elective, but none of them do that because it has the reputation of being the most difficult math course at my school. I'm going into Calc III in the spring, then DE is next...

Homework Statement y'' + y' + y = 1 + x + x2 Homework Equations y = Ʃ CN*xN N starts at 0 y' = Ʃ N*CN*x(N-1) N starts at 1 y'' = Ʃ N*(N-1)*CN*x(N-2) N starts at 2 [b]3. The Attempt at a Solution [/] I know how solve the equations...

Homework Statement Solve the following differential equation: f"(x)=sinx x(0)=0, x'(0)=1 Homework Equations x(0)=0, x'(0)=1 The Attempt at a Solution f"(x)=sin(x) integrate, f'(x)=-cos(x)+C1 f'(0)=-cos(0)+C1=1 => C1=2 C1=2 f'(x)=-cos(x)+2 f(x)=-sin(x)+2x+C2...

The complete question I've been given: The Rossler equations are formally defined as dx/dt=−y−z dy/dt=x+ay dz/dt=b+z(x−c). Let us suppose that a=0.2, b=0.2, c=5.7, x(0)=y(0)=z(0)=0, t∈[0,400]. Let v1(t) be the solution to the given initial value problem, and let v2(t) be the solution of the...

I think I posted in the wrong section and will repost in the textbook/coursework section but don't know how to delete this. Although if you want to answer feel free. The complete question I've been given: The Rossler equations are formally defined as dx/dt=−y−z dy/dt=x+ay dz/dt=b+z(x−c). Let us...

Homework Statement A series RLC circuit has an electromotive force given by E=200e^(-100t) V, a resistor of 80 ohms, an inductor of 0.2 H, and capacitor of 5x10^-6 F. If the initial current and charge on the capacitor are zero, find the current at any time t>0. Homework Equations ...

Homework Statement solve: 160y''=160g-ky y(0)=-200 and y'(0)=0 2. The attempt at a solution I tried to use guess and check to solve this equation, but it didn't turn out nice at all... y''=9.8 - (ky)/160 y''+(ky)/160 = 9.8, guess y=e^(λt), y'=λe^(λt), y''=λ^2e^(λt) : this gives...

Homework Statement Given the ODE y''-ty'+y=0 where y(0)=1 and y'(0)=0 Assume y(t)=Ʃn=0 ( a(n) t^n ) (power series centered at 0) find the general form of the solution ( an=f(n) ) The Attempt at a Solution I used the initial conditions to determine the values a0=1 and a1=0...

Hello Im new here, I hope I'm not disturbing anyone. Following this guide below, I am trying to find two 2. order differential equations, one for q1'' and one for q2'', describing the movement of the double pendulum. I have no problems with the mathematics, but when the guide tells me to...

We know that there are a few forms for 1st order differential equations. Second-order differential equations have an extra term with an x in it. My conjecture is that third-order differential equations have another extra term with an x^2 in it. A friend of mine agrees with this. Is this true and...

Homework Statement Find the indicial roots of the following Differential Equation: xy'' - y' + x3y = 0 Homework Equations y = Ʃ[n=0 to infinity]cnxn+r y' = Ʃ[n=0 to infinity](n+r)cnxn+r-1 y'' = Ʃ[n=0 to infinity](r+r)(n+r-1)cnxn+r-2 The Attempt at a Solution Plugging these values into the...

Dear all, I am interested in solving the following type of system of differential equations for η(x): (1) ∫η(x)ω(x)=0 (2) ∫η'(x)ω(x)=0 for known ω(x), and known limits of the integral. Does this type of equations have a name? Can someone help me to find some reference? Thanks a ton...

Homework Statement \frac{d^{2}y}{dx^{2}} = y\frac{dy}{dx} Homework Equations Let v = \frac{dy}{dx} and v\frac{dv}{dy} = \frac{d^{2}y}{dx^{2}} The Attempt at a Solution The question can be rewritten as: v\frac{dv}{dy} = yv \frac{dv}{dy} = y. (v =/=0 ) This is very easy...

Homework Statement this is the homework that i have to do http://img690.imageshack.us/img690/2783/problemsb.png Uploaded with ImageShack.us The Attempt at a Solution im not really sure if this is the right method but i will solve it like if it was a homogeneous equation by...

Would anyone be able to go through some of the steps for these problems? 1. The birth rate in a state is 2% per year and the death rate is 1.3% per year. The current population of the state is 8,000,000. a) Write a differential equation which models the population of the state. Be sure to...

Hello, I was wondering if anyone could suggest a good book on "beginner's" differential equations. I am at an undergraduate level, it that helps you gage the content. thanks in advance

Hi! I'm working with my PhD thesis at the moment, and I've stumbled upon a pretty involved problem. What I have is a system of equations like this: \frac{dx}{dt} = A \cos(z) \frac{dy}{dt} = B x \frac{dx}{dt} \frac{dz}{dt} = y where A and B are constants. I also have a stochastic term to z...

*URGENT*Damped Harmonic Motion (Differential Equations) A damped harmonic oscillator satisfies the following equation: d2x/dt2 = − 5x − 2dx/dt (a) By assuming a trial function of the form x = A e^qt, determine the solution of this equation "from scratch." Express your final answer as a real...