Differential equations Definition and 999 Threads

Homework Statement A tank contains 2860 L of pure water. A solution that contains 0.04 kg of sugar per liter enters a tank at the rate 5 L/min The solution is mixed and drains from the tank at the same rate. Find the amount of sugar in the tank after t minutes. Homework Equations...

I have always gone along with this, but now I am not so sure: Take the DE: y' +4y = 0 If you carry out the integration, we get y = e^{-4x} +C\qquad(1) but we always pull some stuff like "well since we could write C as ec1, since it's arbitrary", we can write the solution like...

Homework Statement The suspension system of a car is designed so that it is a damped system described by z'' + 2z' + z = f(t) where z is the vertical displacement of the car from its rest position. The car is driven over a (smooth!) road which has "catseye" embedded in the road surface...

Question: A boat of mass m is traveling with the velocity v0. At t=0 the power is shut off. Assuming water resistance proportional to v^n, where n is a constant and v is the instantaneous velocity, find v as a function of the distance travelled. (Note that you need to consider the two cases)...

Hello all! As it turns out, I have a condition that requires me to not be at a physical university this semester, but I would like to try and catch up a bit and also need to make my time off more productive. I would like to take a couple of math courses, particularly Calculus 2 and...

Find equilibrium solutions for the following ODE initial-value problem and linearize the problem about those solutions z" = z − z^3, z(0) = z0 z'(0) = v0 i found the equilibrium solutions to be 0,1,-1. what are the steps to linearize the problem around these?

Homework Statement Find the voltage across a capacitor in an RC Circuit, using [V]_{}[/c] (0) = 1, [V]_{}[/i] n(t)=t. Homework Equations dV/dt = (1/RC)(V)=(1/RC)([V]_{}[/in]) The Attempt at a Solution New to this site: I honestly don't know where to start. Done well in Calculus...

Problem and Equation: Solve dy/dx=-y/(x^2+y) Put into standard form, this is ydx+(x^2+y)dy=0 The only ways of solving differential equations that I currently know are when they are either linear (which this is not), separable (this is also not), or exact (ditto), and I vaguely know about...

Homework Statement y'=y+y^3 Homework Equations The Attempt at a Solution I set y=v, dy/dx = dv/dx. Substituted back into original equation ST dv/dx = v + v^3. Cross multiply, then divide yielded dv/(v+v^3) = dx. After that, I have no clue. The book gives the following...

Homework Statement A particle of mass m = 3kg moves in the xy plane under the influence of a force field having potential φ = 12x(3y - 4x) The particle starts at a point with position vector r = 10i - 10j. a) set up the differential equations and conditions describing the motion. b) solve...

I am a freshman in college and I am in multivariable calculus, I took the first AP calc in high school. I am deciding to walk in on an Ordinary Differential Equations class. It is apparently graduate and I didn't understand a single thing in there. I didn't understand anything mainly because I...

Homework Statement A pond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 gram of this chemical per gallon flows into the pond at a rate of 300 gal/hour. The mixture flows out at the same rate, so the amount of water in the...

New Gravity field differential equations are suggesting to discuss at the Forum. These equations complete Maxwell Equations for Electromagnetic field and make them symmetric. So, Gravity field intensity "g" has dimension of acceleration, it is a vector value. curl g = 0 , this is first...

Let x mg be the amount of drug in the patient at time t. Drug is injected into the patient at a rate of P mg per min The kidneys of the patient remove the drug at a rate proportional to the amount of drug at time t. At a particular point in time, the drug concentration in the patient...

Homework Statement y'' + 3y' + 2y = 24exp(-2x) Homework Equations y'' + 3y' + 2y = 24exp(-2x) The Attempt at a Solution I've solved the characteristic equation and am after the particular solution. I've let y_p = Aexp(-2x), y_p' = -2Axexp(-2x) and y_p'' = 4Axexp(-2x) When...

If we have a DE of the following form: \frac{dX}{dt}=b(t,X_t)+\sigma(t,X_t).W_t and look for a stochastic process to represent the (second) noise term. Now my textbook tells me that the only process with 'continuous paths' is Brownian motion. The noise term denotes random, indeterministic...

Homework Statement Find the general solution of \dot{x} = x + e^{2t}p [/tex] \dot{p} = 2e^{-2t}x - p Homework Equations The Attempt at a Solution I know how to solve systems with constant coefficients using eigenvalues and eigenvectors, but what should I do in this case?

Hello guys, I have these two questions that I spent s much time to solve them but couldn't. solve the given differential equations or initial-value problems * dy/dx = x/t * dy/dt = 3 + 5y It's about SEPARABLE FIRST-ORDER DIFFERENTIAL equations. Thank you so much,

Hey guys, I am new to PF. I need to be able to model a stiff differential equation in MatLab. I haven't used MatLab before so I am not really sure how to set the function and boundary conditions for the equation: y'' + (2/x)*Y' = (.7/x^2)*( (y^(-1/2)) - (.067)((1-y)^(-1/2) ) y(0)=0...

Homework Statement I attached the problem in a picture, I'm not so good at making it show correctly on here. Homework Equations The Attempt at a Solution I'm really unsure of what to do with this problem. I don't know where to start. Can someone please try to guide me through it...

good day everyone. i need to know what test must i make first in dealing with differential equations.. please help me. it's hard for me to figure out whether an equation is homogeneous or exact... there are examples of exact differential equations that have same degrees for M(x,y) and...

Next year I'll be entering my first year in college, and I'm not sure if I should skip Calculus 1 and Calculus 2. I have both credits from my AP scores, I'm much more confident in my Calc 1 skills than Calc 2, because I don't really remember anything from series and sequences really... I'm...

Homework Statement A 300-gal capacity tank contains a solution of 200 gals of water and 50 lbs of salt. A solution containing 3 lbs of salt per gallon is allowed to flow into the tank at the rate of 4gal/min. The mixture flows from the tank at the rate of 4 gal/min. The mixture flows from the...

Homework Statement newbie here.. Blood carries a drug into an organ at the rate of 3 cm^3/sec and leaves at the same rate. The organ has a liquid volume of 125 cm^3. If the concentration of the drug in the blood entering the organ is .2g/cm^3, what is the concentration of the drug in the organ...

Homework Statement Determine whether the given first-order differential equation is linear in the indicated dependent variable by matching it with the first differential equations given in #7. Homework Equations #7 (sin \theta)y^{'''} - (cos \theta)y^{'} = 2 #10 (u)dv +...

Hi everyone... I need to solve the differential equations of a RC circuit given a voltage and a current pulse. I have to get this responses: http://i.imagehost.org/view/0340/Respuesta1 I'm using matlab, with runge kutta. I've been solving the equations separately changing the initial...

Hello, Could you please help me to solve the differential equations analytically? dvy/dt = - (k/m) * vy - g dy/dt = vy vy = vo*sin(theta) = vy, y = yo

Homework Statement A curve passing through (3,-2) has a slope given by (x^2 + y^2)/(y^3 - 2xy). Find the equation of the curve. Homework Equations The Attempt at a Solution My first thought was to plug in the points (3,-2) into the slope equation and plug them into the line...

Homework Statement A spring mass system has the equation of motion: c1e^(-t)*sin(t) + c2e^(-t)*cos(t) + 3*sin(t) Is there damping in the system? Is there resonance in the system? The Attempt at a Solution If I had to guess I would say that the 3*sin(t) at the end of the equation...

Hello, Can you give some suggestions to solve the following system of 1st order nonlinear differential equations? Thank you. \[ \begin{array}{l} u'(t) = Au^2 (t) + B(t)u + C(t) \\ u(t) = \left[ {\begin{array}{*{20}c} {x_1 (t)} \\ {x_2 (t)} \\ \end{array}} \right] \\ A = \left[...

in a scientific study, the size , p of a population at t hours is being studied. Initially p = 560 and after 6 hours, p is found to be 1218. In a simple model of population growth, the rate of the population is taken to be proportional to the population at that time. Using this model predict...

Homework Statement Hey Everyone, Here is a problem from my book that has my confused. I really don't understand what it wants me to do so if anyone could give me a few hints it would be greatly appreciated. I am doing problem 34, but I included 33 since it wanted to follow the same method...

Linear Algebra and Vector Analysis for Engineers Methods of Differential Equations This fall I might be able to take both courses. According to our school's sample curriculum, both courses are taken simultaneously in upper sophomore year (spring). Of course it is upon the decision of the...

hello all, I need two solutions to two different tensor diffeqs. I think I may have the solution to the sourceless equation, however I am in the dark about the one with the source. \left(\partial_{\gamma}\partial_{\alpha}+\imath k^{\beta}g_{\alpha\beta}\partial_{\gamma}\right)...

Homework Statement The equation \frac{dy}{dx} = A(x)y2+B(x)y+C(x) is called a Riccati equation. Suppose that one particular solution y1(x) of this equation is known. Show that the substitution y = y1+\frac{1}{v} transforms the Riccati equation into the linear equation \frac{dv}{dx}+...

Hi all, I want to solve equations of the form: \dot x + x + y = sin(\omega t) \dot y = \dot x - y This is not a standard type of form for Runge-Kutta or linear systems of equations because \dot y = f(\dot x, y, t) instead of \dot y = f(x, y, t). Any hints or links to place for...

hi i got the eigen values as e=-1, e=i, -i as the imaginary roots and both 1 multiplicities can some one complete the question please thanks

I was wondering if anyone has any good resources for differential equations? I've been using Paul's Notes all semester but they don't cover the last chapter of my book. The chapter is Nonlinear Differential Equations and Stability. The topics are The Phase Plane: Linear Systems, Autonomous...

I've been working with this problem for almost two weeks trying to find a good equation for the decay of Bismuth to no avail. Can someone give me insightful comments: Here's the problem: Homework Statement In the radioactive decay series of Uranium (238, 92), isotopes of lead...

xy'' + y' = 0 Is it ok to multiply this whole equation by x to make it a cauchy-euler equation?

Homework Statement What method would you use to solve DE's of this type R'' + R' +R[(constants) + e^(-R^2)] = 0 ? Homework Equations The Attempt at a Solution

1. Find all real solutions: (dx/dt)-2x=cos(3t) Homework Equations 3. I really don't know where to start here. Any advice to get me on my feet would be appreciated.

Homework Statement Find the particular solution to the differential equation using method of variation of parameters: 4y''-4y'+y=16e^(t/2) The Attempt at a Solution Set 4y''-4y'+y=0 then the homogeneous solution is: y= c1*e^(t/2)+c2*te(t/2) set y1= e^(t/2), y2= te^(t/2)...

Homework Statement Suppose that f:R->R is twice differentiable and that f''(x) + f(x) = 0, f(0)=0 and f'(0)=0 Prove that f'(x) = f(x) = 0 for all x Homework Equations The Attempt at a Solution I can solve this using methods from calulus, using an auxillary equation and the...

Homework Statement My professor states that a differential equation of form y'(x)=f(ax+by+c) can be reduced to a separable equation by substituting in v=ax+by+c, but I don't see how. Edit: more specifically: y'(x)= sqrt(3x -4y +2)Homework Equations y'(x)=f(ax+by+c) v=ax+by+c The Attempt at a...

Hi guys, So I have gotten my assignment for my DE class and fortunately for me, someone had already posted up the questions on the net. Here it is: http://www.cengage.com/math/book_con...e/Project3.pdf I have posted this in the DE section, which i think is the wrong section to post in...

Homework Statement Water flows from a conical tank with circular orifice at the rate \frac{dx}{dt} = -0.6*\pi*r^2\sqrt{2g}\frac{\sqrt{x}}{A(x)} r is the radius of the orifice, x is the height of the liquid from the vertex of cone, A(x) is area of the cross section of the tank x units above...

Homework Statement using the power series method (centered at t=0) y'+t^3y = 0 find the recurrence relation Homework Equations y= \sum a_{n}t^{n} from n=0 to infinity y'= \sum na_{n}t^{n-1} from n=1 to infinity The Attempt at a Solution I went through and solved by putting the...

Homework Statement a) ẍ + 5ẋ + 4x = 0 x(0) = 0, ẋ(0)=1 What type of damping? b) ẍ + x = cos(t) x(0) = 0, ẋ(0)= 1 What type of motion? The Attempt at a Solution a) Let x = R Eᴿᵀ R = -4 R = -1 x(t) = CE**-4T + DE**-t C + D = 0 -4C - D = 1 C = 1/5 D = 1/5 And it is...