Differential equations Definition and 999 Threads

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...

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...

Help pls decide this Differential Equations!I did not coincide with the answer and in some no idea how to do! will be very grateful if you start a proper solution to Us 1) y(4)+2*a2*y''+a4*y= cos(ax) 2) y' = x + 1/y; y(0)=1 3) y' = 2*x + cos(y); y(0) = 0 4) y(x) - λ*(0 to...

Hey, I need your help to solve the following set of coupled differential equations numerically. dn(t,z)/dt=I^5(t,z)+I(t,z)*n(t,z) dI(t,z)/dz=I^5(t,z)-α(n(t,z))*I(t,z) where I(t,0)=I0*exp(-4ln2(t/Δt)^2) and n(t,0)=0 and n(-certrain time,z)=0. Some constant parameters I did not show...

Help pls decide this Differential Equations!I did not coincide with the answer and in some no idea how to do! will be very grateful if you start a proper solution to Us 1) y(4)+2*a2*y''+a4*y= cos(ax) 2) y' = x + 1/y; y(0)=1 3) y' = 2*x + cos(y); y(0) = 0 4) y(x) - λ*(0 to...

Homework Statement Be able to write a system of Linear homogenous differential equations as a matrix differential equations. Homework Equations The Attempt at a Solution I have uploaded the work and original problem. My question is did I properly answer this question?

Homework Statement Find the general solution to the system of differential equations. Homework Equations The Attempt at a Solution I uploaded the original equation and my work so see the attachment. I want to know how they got the vectors the got typically when I have done 2x2...

Homework Statement finding the general solution. I would like to know if the 20-e^x will be treated as a sum of a polynomial? Homework Equations The Attempt at a Solution

Homework Statement Denote by L(t) the length of a fish at time t, and assume that the fish grows according to: dL/dt = k(34-L(t)) with L(0) = 2 a) solve the above equation b)Use your solution in part a to determine k under the assumption that L(4) = 10. c) Find the length of the fish...

Homework Statement I uploaded the problem statement please see attachment for original problem. The problem number is 4. Homework Equations The Attempt at a Solution For clarity I uploaded what I have done please see the attachment with my work on it. I am not sure if I am doing...

Homework Statement Show the origin is the only critical point Homework Equations x'= -x-x3 y-= -y-y5 The Attempt at a Solution I'm not really sure how to go about this. I missed a few lectures due to a medical issue, and now were at the end of the semester and I can't get in touch with the...

So, I'm learning how to solve LR, RC, LC etc. types of circuits using differential equations. I understand how to do the math with differential equations, but I am confused as to why the variables are split in the way they are. For example, for an LR circuit you have the equation...

I'm going to be taking a class in ordinary differential equations over the summer and have about 2 weeks to prepare. The class has linear algebra as a prerequisite, and I just wanted to know what I would need to review from linear algebra to prepare myself for the course?

Homework Statement Find the eigenvalues and the eigenfunctions for x^2y"+2xy'+λy = 0 y(1) = 0, y(e^2) = 0 Homework Equations See problem The Attempt at a Solution My book has one paragraph on this that does not help me. I tried using an auxiliary equation and solving for lambda...

http://dl.dropbox.com/u/33103477/Linear%20oscilator.png I am having trouble understand the question, what I have done its solve the equation using the substitution x=e^{rx} Then, I have the solution given by: x(t)=c_1 e^{t(\sqrt{\gamma^2 - \omega^2 })} + c_2e^{-t(\sqrt{\gamma^2 -...

I need to NDsolve four differential equations. But I find my code does not work. Who can give me some suggestions? Thanks!

Hi,I'm new to these and thus my question might sound stupid: Do differential equations ALWAYS have just one or zero general solutions? I know each diff.equation can have multiple particular solutions, but can it only have one or zero general solutions?

Homework Statement The Attempt at a Solution So I've been interpreting the information in the problem as follows: F_{damping} = 4u' = μ(u'), k = \frac{4N}{m}. If the system is critically damped then μ = 2\sqrt{km} = 2\sqrt{\frac{4N}{m}m} = 2\sqrt{4N}. Now it seems as though the spring...

I've come across an issue that was bugging me last semester in my circuits class today: Finding general solutions of linear differential equations. Just add the homogeneous and particular solution and it's done. Last semester it wasn't explained why exactly this is possible and this semester...

Homework Statement Solve the matrix of differential equations with given initial values. dx/dt= (-6 2) x (-3 -1) Initial value is x(0) = -2 -5 Homework Equations (A-λI)=o The Attempt at a Solution My eigenvalues are -4 and 3 My...

Hi, I have problems rewriting equations with the term y'' as a system of first order differential equations. I've been given several equations and was told to write them as 1st order DEs, then calculate the numerical solution using the Euler's modified method. I know that y'=f(x,y), so if...

Homework Statement Solve the ODE with the boundary conditions given Q''+Q = Sin(2x) where Q(0) = 1 and Q'(0) = 2 So i know i need to solve the general and particular solutions, however, I am a little confused. Any help or advice would be great, Thanks in advance. Homework Equations Y...

Hello to everybody, I'm very new to solving ODES and equations with MATLAB. I have been asked to solve a system of nonlinear equations for simulating the growth of a solid tumor. Assuming that we have the 5 unknowns which are dxd arrays: f,g,m,p and n. f(x,t) is the volume fraction of tumor...

Homework Statement So in my notes it says that the general solution to a system of linear equations: x1'(t) = a11x1(t) + a12x2(t) x2'(t) = a21x1(t) + a22x2(t) is: x(t) = c1eλ1tv1 + c2eλ2tv2 What I don't understand is how you go from the system of equations to the general solution, the notes...