Differential equations Definition and 999 Threads

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!

Hi I am trying so solve a set of coupled ODE's. I have been able to get a solution from Mathematica using NDSolve, but when I change the coefficients an error appears: "NDSolve::mxst: Maximum number of 10000 steps reached at the point t == 0.0000748339914040257`. >>" I have tried...

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...

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...

Would someone be able to help me with the question Life cycle of butterfly is egg -> caterpillar -> butterfly. Each week 5% of the eggs will hatch and 2% of the caterpillars will turn to butterflies. You start with 100 eggs and 60 caterpillars. Using calculus to obtain an equation...

I am not sure I understand Linear and non-linear differential equations properly so I will ask some question which someone will hopefully answer. Is dx/dt = x + 2 a linear differential equation? If so does this mean that the rate of change of is constant? Is dx/dt = x^2 + 4x a non linear...

Hi. I'm not sure if this is the right place for this kind of question, but it's related to coursework. I took Calc III during senior year of high school and linear algebra during freshman first semester. Then, I haven't taken any math class because I tried to fill my prereqs out and also take...

Hello, In my study i came across to solve the analytical solution for coupled equation y(x,t) and z(x,t).The equations contains" f " function which is a function of the first variable exponentially. The first equation is : ∂y/∂t=∂^2(y)/∂x^2- 2*f(y)*z; The second equation ...

Hello I know nothing about differential equations, can you explain them to me in a few simple words? And what's so special so we study them seperately? Thanks

I'm looking for a good resource about modelling for differential equations. I've completed two courses on ODE's and PDE's, but they both lacked in the applications/modelling department. Can anyone recommend a good resource/book on modelling?

Hey Can I have your help with: 1. (2e^y - X)y'=1 y(0)=0 y(x)=? 2. xyy' + y^2 - x^2 = 0 3. x^2y' - 1 = cos2y lim y(x) = π/2 x->+∞ thanks

Hello every one, In my physics problem, i end up having two coupled second-order nonlinear differential equations where the coupling terms include, the variable, the first derivatives, and also a second derivative coupling. I appreciate any help on how to handle this system before setting it...

Homework Statement Show that w(t) = tanh(t) solves the nonlinear problem: w''(t)+2w(t)-2w3(t) = 0 t ε ℝ Homework Equations \frac{d^2tanh(t)}{dt^2} = -2tanh(t)sech2(t) = \frac{-8sinh(2t)cosh^2(t)}{(cosh(2t)+1)^3} tanh(t) = \frac{sinh(2t)}{cosh(2t)+1} tanh(t)3 =...

Hello, I am trying to tackle a word problem in differential equations, but the setup has flummoxed me. Thank you in advance to any advice/help given. Homework Statement Beginning at time t  0, fresh water is pumped at the rate of 3 gal/min into a 60-gal tank initially filled with...

Hello everybody! This is the first post for the differential equations tutorial. Unlike the one on MHF, I've decided to take this project a little more seriously and have taken on the task of making a book based on these posts (well, it's really the other way around - the posts will be the...

I'm a college student whose been force enrolled in Linear Algebra and Differential Equations. No offence to math lovers but I don't find them very interesting. I study much better in courses which I find interesting so could someone please point out interesting applications of L.A. and D.E...

Homework Statement Find all eigenvalues and eigenfunctions: -y'' (x) = \lambda y(x) , x \in (a,b) y(a)= y(b) =0 . Homework Equations sin x = \frac{e^{ix} + e^{-ix} }{2i} . The Attempt at a Solution So actually the only problem I have is to find the eigenfunctions (which should...

Hello all, I am dealing with a rather complicated problem (as we all do), without much knowledge in differential equations. I have coded a numerical solution, taking a straightforward approach: constructing the functions step by step, but I would like to try to achieve better precision...

Matlab -- How to solve simultaneous non-linear differential equations? How to solve simultaneous non-linear differential equations in MATLAB m-file without using the commands?. can you give me the program?.

Consider the differential equation where I''+I=e^it where i= sqrt (-1) So I don't know what to do. I do know that The second derivative of c*t*e^(i*t) is -c e^(i t) (-2 i+t) But I don't know what to do for a and b and I need help to get threw this problem before I take my test...

This isn't a homework problem, but it's a problem I've come across that I would really like to know the answer to. Is it possible? Homework Statement Solve for u(x) and v(x) in the system of equations: u(x)v'(x) = x^x(ln(x) + 1) u'(x)v(x) = x^xln(x) 2. The attempt at a solution...

Deriving Probability Density Functions from Partial Differential Equations? Hiyas, I have been told that it is quite normal to get PDFs (Probability Density Functions) from PDEs (Partial Differential Equations). That in PDEs that the function can be a PDF and you can get this by solving the...

I am looking for the solution of C_{3.p}(t) Edit: sorry I forgot to add the explantions for the symbols as HallsofIvy pointed rightfully out. - There are n+m+p equations with n+m+p variables of C - A, B, C, D, E, n, m, p are constantsusing the following set of equations: Part I \frac...

And not taking ODE's? Is this doable? I understand the basics of most concepts as I am currently self-learning from online resources and textbooks, but I decided not take the class during the summer as I'm already taking calc III. The problem is that when the year starts up again PDE's is taught...

When differential equations are being developed, what dictates the order of the differential? What decides if it is second order, third order, fourth order, fifth order, etc... I understand that the process is taking the derivative of a derivative of a derivative, but what decides if the the...

Dear, I work as a process engineer and haven't had to use differential equations or integrated anything for years. I have the following physical problem and please advice me if this is not the correct location on the forum. Believe me or not but this problem has been researched for over 20...

I've been reading through my mechanics of materials textbook recently, notably in regard to the section on the deflection of beams. The well regarded Euler-Bernoulli beam theory relates the radius of curvature for the beam to the internal bending moment and flexural rigidity. However the theory...

Homework Statement Solve using an appropriate substitution ydx+(1+ye^x)dy=0 Homework Equations N/A The Attempt at a Solution u=y du/dx=dy/dx u+(1+ue^x)du/dx=0 This is where it gets really sticky for me. I can't see it being a separable variable problem because it seems...

Homework Statement Solve the following initial value problem: \frac{d^2y}{dt^2} + 2 \frac{dy}{dt}+y = t y(0) = 1, \ y'(0) = 0 The correct answer must be: y(t)=3e^{-t} + 2 t e^{-t} + t -2 The Attempt at a Solution Where did they get the term 2te-t from? Here's how I've done it so far...

We have this system of equations: \begin{cases} x'= -x + 2y & (1)\\ y' = -2x - y + e^{-t} & (2) \end{cases} where x(0) = 0 ; y(0) = 0 We apply the Laplace transform on (1) and (2) and get: (s + 1)X - 2Y = 0\\ 2X + (s + 1)Y = \frac{1}{s + 1} We can use elimination here...

Solving linear differential equations by "factoring" I have thought of an interesting way of solving n-th order linear differential equations (with constant coefficients) by imitating the way we solve n-th order polynomials, that is by "factoring" it into a "product" of simple 1st order linear...

Homework Statement A cell contains a solute at a concentration of Ct and the concentration of the same substance outside the cell is a constant, k. By Fick's law, if ct and k are unequal, solute moves across the cell wall at a rate proportional to the difference between ct and k, towards the...

Fill in the missing values in the table given if you know that dy/dt=0.2y. Assume the rate of growth given by dy/dt is approximately constant over each unit time interval and that the initial value of y is 6. Table: t-0-1-2-3-4 y-6-?-?-?-? (fill in the missing values where there is a...