Diff eq Definition and 271 Threads

\acute{y} = \frac{1}{t^{2}} -\frac{y}{t} - y^{2} To solve a Riccati type diff eq a particular solution is needed. In our case it is: y_{1} = -\frac{1}{t} By setting y= y_{1}+\frac{1}{u}= -\frac{1}{t}+\frac{1}{u} and differentiating this \acute{y}= \frac{1}{t^{2}}-\frac{u'}{u^{2}}...

I'm working on a project where I'm trying to find the differential equation of a falling raindrop. The drop I'm considering will be under 10mm to eliminate the drops breaking apart and I've found that for that size, the drops will be spherical and traveling 6-8m/s. I've determined my air...

Homework Statement find 2 power series solutions of the given diff eq about the ordinary point x = 0 y'' - xy = 0 Homework Equations y = (c_0)(y_1)[x] + (c_1)(y_2)[x] The Attempt at a Solution i can set it up to this (sorry idk out how to insert the subscripts with the summation symbols)...

Hey all, So I need some advice on my differential equations course. Last semester I took Calc 3 and loved it. I loved that I could visualize everything. It made math seem so much more concrete. On the other hand, there is differential equations. Now I know that there are an immense amount of...

Homework Statement An object in free-fall has an acceleration (which is the rate of change in velocity with respect to time) of 32.2 feet per second2 downward plus air resistance. The air resistance is proportional to the velocity squared. If the initial velocity is 0 feet per second and the...

Homework Statement Say we have a warehouse with a 5 hr time constant. The outside temp is 16C at 2:00AM, and 32C at 2:00PM. The warehouse is at 24C at noon. What will the temp be at 6:00 pm? When will the temp be 27C? The Attempt at a Solution First, I set up a sine wave for the...

I know you guys must get tired of the tank problem, but I just can't seem to get this figured out. This is my first post here, so hopefully this is in the right subforum and is presented properly. "A brine solution of salt flows at a constant rate of 4L/min into a large tank that initially...

Homework Statement This is part of a solution to a E&M example from a book. I am in the middle of following the solution and I come across this system of diff eq's:y''=\omega z' z''=\omega (\frac{E}{B}-y')Homework Equations Solution according to author is: y(t)=C_{1}\cos (\omega t)+C_{2}\sin...

Homework Statement \frac{dy}{dt}=r(1-\frac{y}{K})y Homework Equations The Attempt at a Solution 0=r(1-\frac{y}{K})y y=0 and K. Plotting dy/dt vs y, the intercepts would then be (0,0) and (0,K). The book says "the vertex of the parabola is (K/2, rK/4)." Is this something...

dv/dt=g-(k/m)*v^2 i thought about all sorts of diff eq solving techniques but nothing comes up to my mind dv/(g-(k/m)*v^2)=dt but it doesn't really help ...

Homework Statement Solve each of the following initial value problems and plot solutions for several values of y_0. a) dy/dt=-y+5, y(0)=y_0 b) dy/dt=-2y+5, y(0)=y_0 c) dy/dt=-2y+10, y(0)=y_0 Homework Equations - The Attempt at a Solution I have solved all of the equations for...

Fluid is entering a patient at a rate r, given in cm^3/hr, and a drug is present at some amount of mg/cm^3, m. The drug is absorbed or leaves at a rate given in h^(-1), c, proportional to the amount of the drug. I want to write a differential eq describing amount, a, in terms of t. I...

Ok...so this isn't homework (well past that at 39!) but I'm trying to brush off the old cobwebs and solve a vehicle motion problem. Specically, I'm trying to find the Homework Statement Ok...so this isn't homework (well past that at 39!) but I'm trying to brush off the old cobwebs and...

Homework Statement Find the Fourier series of f on the given interval: EDIT: For the result of an, it should be multiplied by \frac{2}{1+n^{2}}. That has been corrected.

Homework Statement The problem can be found here: http://alex.fangsoft.net/math.pdf I have completed Task #2, it is Task #1 that I am very lost on. Our teacher has really thrown us head first into the water with this one, I am very unfamiliar with differential equations and their...

Diff Eq. Easy question on prob. Please help...last step Homework Statement Solve The Attempt at a Solution So this is my attempt. I just need to figure out how to adjust Y(s) so I can take inverse laplace transform. I have made the denominator a single fraction, whose denominator is s2+1 and...

Homework Statement The initial mass of fish in a lake was 7 thousand pounds on January 1st, 2001. Since the time, there was a 4-year moratorium on the harvesting on this specific type of fish. This species of fish reproduce at a rate proportional to the mass and by next year on the same...

Homework Statement I have the following DE: y'' + x^my = 0Homework Equations Maybe Frobenius or Power series or Bessel.The Attempt at a Solution I am having a hard time nailing down the type of DE this is. Clearly it is 2nd order homogeneous with variable coefficients. If m is a *...

Hello all, I have been assigned a project to create artwork using differential equations, the obvious idea would be to use Mathematica or Maple to obtain general solutions and replace values to obtain different level curves and then fill in the space between them. However, I'm wanting to...

Homework Statement I was given: x\sqrt{x^2 - y^2}\,dx = (x+y)(y\,dx - x\,dy)\qquad(1) \Rightarrow x\sqrt{x^2 - y^2}\,dx = xy\,dx - x^2\,dy +y^2\,dx - xy\,dy Dividing by dx we have x\sqrt{x^2 - y^2} = xy - x^2\frac{dy}{dx} +y^2 - xy\frac{dy}{dx} \Rightarrow x\sqrt{x^2 - y^2} -xy - y^2 =...

I just realized I won't have the chance to take a class in differential equations before I have to submit my math graduate school applications, so there's no way I'll have the class beforehand. I've taken pretty much every other topic mentioned, and will review heavily on the calculus (it's been...

Diff eq, Spring/mass damped/driven--Am I doing this right?! Homework Statement 1.) After a 10lb weight is attached to a 5ft spring, the spring measures 7ft. The 10lb is replaced with 8lb, and placed in a medium offering resistence equal to the instantaneous velocity. A) find the equation of...

Homework Statement Solve the given differential equation by using the substitution u=y' y''+(y')2+1=0 The Attempt at a Solution If I got to this last integral correctly, I don't know how to solve it. I'm thinking I didn't get to that step correctly.. But I can't find my mistake..

So I had an exam and got this problem wrong, that I had done incorrectly on the quiz as well. comments in red under picture are comments from professor. here is the work: Attempt) Why is this general solution? What is the fundamental set? What is yp? (this should be verified) So on the...

given x(t)=impulse find y(t) y(prime)=4y=8x i am lost

Homework Statement Solve using Method of Undetermined Coefficients: y'' - 2y' + 3y = 15t - 8 The Attempt at a Solution First I used the characteristic equation to solve for the homogeneous solution to get: yh = C1e-t + C2e3t Great. Now I need to find the particular. I am...

[b]1. Given i. dx/dt + y = 0; x(0) = 1 : ii. dy/dt + x = 0; y(0) = 0 Solve for the solns of x and y Although these are first order dif eq's I worked them as leading to a second order undetermined coefficients problem First I wrote them as i. x' + y = 0 and ii. y' + x = 0 Eqn. ii...

Homework Statement y(5) - 2y(4) + y(3) = 0 This is 5th-order, linear, HG, with constant coefficients, and hence I used the characteristic equation: m5 - 2m4 + m3 = m3(m - 1)(m - 1) = 0 Hence, m = {1,1,0,0,0} and so the solution is given by: y(x) = C1 + C2*x +C3*x2 +...

Homework Statement Here is my issue. I am an EE student that has been part time for almost five years. I took diff eq and signals a long time ago. I am currently taking a feedback and controls class, and my lack of memory in these topics is killing my study time. I am looking for relevant...

Homework Statement Consider the case of a rocket taking off vertically from rest in a gravitational field g. The differential equation is given by m\dot{v} = -\dot{m}v_{ex}-mg Assume the rocket ejects mass at a constant rate, \dot{m}=-k (where k is a positive constant), so that m=m_{0}-kt...

So its not a problem, but a step in an example that I need explained. The section is solutions by substitutions and its an example of solving a homogeneous DE. Step goes from: \left(x^{2}+u^{2}x^{2}\right)dx+\left(x^{2} - ux^{2}\right)\left[udx + xdu\right]=0 to: x^{2}\left(1 + u\right)dx +...

Homework Statement Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. Homework Equations dy/dx + 2xy = 1; y = e-x2\int(from 0 to x)et2dt + c1e-x2 The Attempt at a Solution...

Homework Statement Salt water pours into a 10 liter tank at a rate of 4 l/min. Its concentration is 2 g/l. The brine in the tank is well mixed and it drains out at a rate of 4 l/min. Call y the grams of salt in the tank at time t. The tank is initially full of fresh water. Solve the...

So my engineering program has me taking LA and Diff. Eq. in the same semester, after Calc II and before Calc III. I don't understand why that is...what would be the idea behind this?

Homework Statement Find the general solution of \frac{dy}{dt} = 2y +sin(2t) Homework Equations The general solution of a nonhomogeneous ode is the particular solution of the nonhomo plus the solution of the homogeneous ode.: y(t)= y_{p}(t)+y_{h}(t) The Attempt at a Solution...

So I am an engineer and its been about two years since I have taken a differential equations class and the method in which to solve this has totally been lost to me. If anyone can help me out that would be great thanks. m1x1''+k(x2-x1)+b(x2'-x1')+F(t)=0 m2x2''+k(x1-x2)+b(x1'-x2')=0 I...

Homework Statement Find a general solution for y''' - 6y'' + 9y' = 0 Homework Equations The Attempt at a Solution I know that the general solution for a homogeneous DEQ is Y(x) = c1y1(x) + c2y2(x) ... cnyn(x) however, I am not given y1, y2 , or y3 so I am to assume that the...

Is it?

Wanted to brush up on my diff equations a bit. I have kind of forgotten how to determine phase plane stability in systems of differential equations. Homework Statement Solve linear systems. Determine whether the critical point (0,0) is stable, asymptotically stable, or unstable. dx/dt=2x...

Has anyone used Apostol's 2nd edition textbooks for Calculus? They contain lots of information about linear algebra and differential equations. But do they contain enough to be equivalent to a first and/or second course in them? If they do not, what supplementary texts do you recommend to...

Homework Statement Hey all. I'm having issues with a few Diff. Eq. problems. I think I'm screwing up at the point of u-substitution, but I do not know for sure. Homework Equations I'm evaluating: (x2 + x3)*integral (x4/(x4+2x5+x6) The Attempt at a Solution I eliminate x4 inside the...

Newton's Law of Cooling (diff eq. -- separation of variables) Homework Statement Fresh coffee sitting in a room cooling...you know the routine. Anyhow T(0) = 90degreesCelcius. Room temp=25degrees Celcius find k. Then he asks us to use Euler's method to estimate coffee temp after five...

figured it out, thanks Figured it out, thanks.

Hello PF, maybe you can help with this one! I need to show that the Laplace transform of J0(at) is (s^2 + a^2)^-1/2. My prof told me to start with the form: x2y'' + x y' + (x2 + p2)y = 0, where p = 0 ITC. What have I got so far?... Doing the Laplace transform on both sides, where Y...

Homework Statement My professor wants us to derive a differential equation for the current in a circuit. The circuit has a battery with voltage E, resistor with resistance (iR)??, and inductance L. It's in series. The Attempt at a Solution What REALLY confuses me are these things...

I need help. For the following problem, can someone suggest how I should start on this question. I only have one quarter of diff eq classes plus a few classes in Fourier analysis. I'm out of my league. Consider a box with length, width and height given by L. The box encompasses the region...

Find the solution of: y" + 3y' = 72sin(3t) + 36cos(3t) where y(0) = 6 and y'(0) = 9 I first found the solution to the homogeneous eq: the roots (R^2 + 3R = 0) are R = 0, -3 which gives the family of solutions: y = a(1) + be^(-3t) and y' = -3be^(-3t) using the initial conditions...

Homework Statement The following problem involve the setting up and solving of a first-order differential equation for a physical situation. Once, derived the equation itself is not difficult to solve. A boater rows across a straight river of constant width "w", always heading (i.e., pointing...

Homework Statement Given: dx/dt + 3*x = exp(-3*t) and all initial conditions are zero. Homework Equations Laplace The Attempt at a Solution L[dx/dt + 3*x = exp(-3*t)] s*X(s) + 3*X(s) = 1 / (s + 3) X(s) = 1 / (s + 3)^2 So here is where I get mixed up. For some reason, I thought I was...

I was wondering if anybody could refer me to a few good differential equations books? I took an intro to diff eq class, but due to my job changing my work hours to the same time as the class I didn't get the full experience of the class (i got a B, but I don't really understand the material it...