Differential equations Definition and 999 Threads

How to solve a system of 200 second order differential equations in matlab? I know simulink can work but it takes damn long time to draw those blocks for 200 equations...

How does one go about dealing with a linear differential equation with random but constant coefficients (e.g. X''(t) + A*X'(t) + B*X(t) = 0 where A and B are random variables, but are constant with time)? I've searched for things like random differential equations and stochastic differential...

Homework Statement This is actually a question we went over in class, but I kind of spaced out when my teacher was explaining it. I have since solved it myself while I was reviewing for my calculus test, but when I compared my answer with the answer key my teacher provided to our class, I...

[SIZE="4"] an object is dropped from a height of 500m. when will object reach the ground level and with what speed? important: the solution must be by: Differential Equations.

Homework Statement A tank initially contains 180 gallons of water in which 8grams of salt are dissolved. Water containing 9 grams of salt per gallon enters the tank at the rate of 3 gallons per minute, and the well mixed solution leaves the tank at the rate of 1 gallon per minute. The...

Suppose there is an ant at each of the four corners of a square with side length 1, such that (0,0) and (1,1) are at opposite corners of the square. The ant at (0,0) is facing the ant at (1,0) is facing the ant at (1,1) and so forth. Each ant will choose its path such that it is always facing...

Suppose I have a third order differential equation, and have three solutions, y1, y2, y3. I can check to see if they are linearly independent as such: if their wronskian is non-zero, they are linearly independent. But the wronskian is just a determinant of a matrix. y1 y2 y3 y1' y2' y3' y1''...

Hi! I'm a student at a community college and I'm getting an AA in physics to transfer to a university. I eventually want to apply to medical school with a bachelors degree in physics. I've recently been going over the classes required for medical school and for the physics major. I've...

Homework Statement I need to solve for a general solution of the following equation: (x^2+6x+12)dy=y^2dx 2. The attempt at a solution I tried using the method for seperable ODEs and got the following: ∫(x^2+6x+12)dy=∫(y^2)dx (x^2+6x+12)y=(y^2)x+C (x^2+6x+12-C)/x=y

Homework Statement yy''+(y')2 = 0 Homework Equations yv(dv/dy)+v2=0 The Attempt at a Solution Variable separable when solving for the first step the result is: - ln |v| = ln |y| + C1 Now, I've looked at the remainder of the solution with a few other sources and the cause of...

Homework Statement solve (y^15)x(dy/dx)=1+x using the initial condition y(1)=3 express y^16 in terms of x Homework Equations The Attempt at a Solution i change the equation to the form y^15 dy = (1+x)/x dx integrating both sides i got y^16/16=x+lnx+C To solve...

Homework Statement Find the general solution and any singular solutions to (2xy^3+4x)y'=x^2y^2+y^2.Homework Equations The Attempt at a Solution 2x(y^3+2)y'=y^2(x^2+1) \int\frac{y^3+2}{y^2}\,dy=\int\frac{x^2+1}{2x}\,dx \frac{y^3-4}{2y}=\frac{x^2+2\ln x}{4}+C Is this correct? To find the...

at t=o an evenly mixed 40 liters solution with 100grams of salt is poured into a container. solution comes in at 2 grams per liter at 3 liters per minute and flows out at the same rate. At what time is the salt solution 120 grams? I got -9.something minutes for my answer :/ This question was...

I am greatly struggling with a homework assignment given out by my physics professor. It mostly differential equations but based on spring physics. I'll type out the first couple parts but will most likely need help with more as I get farther. Homework Statement Y(t) : the y position of mass...

I am signing up for my third quarter of college classes soon and I have to choose if I am going to take Differential Equations or Matrix Algebra this quarter. I am given the option to take either of them and I do not know if I will be able to take the other one anytime soon. Which of the two...

Find the solution y = φ(t) of the given problem and evaluate φ(t) at t = 0.1, 0.2, 0.3, and 0.4. 1.y'=3+t-y y = φ(t)=t-2e^-t y(1)= 0+(0-2e^0)*(.1)=.8 and the correct answer is 1.19516 2. y'=2y-1 What I'm getting stuck on is do I use the formula y(n)=y(n-1)+f(t(n-1),y(n-1)h because...

Homework Statement Solve the following differential equations by series and also by an elementary method and verify that your solutions agree. (x^2+2x)y''-2(x+1)y'+2y=0 Homework Equations y=\sum_{n=0}^{\infty} a_nx^n y'=\sum_{n=1}^{\infty} na_nx^{n-1} y''=\sum_{n=1}^{\infty}...

Homework Statement Given that a population, P, after t months, can be modeled by the logistic model dP/dt = .3 P (3.5 - P/40). P(0) = 30 a) Solve the diff eq b) Find the population after 2.5 months c) Find lim P(t) as t -> infinity Homework Equations P(t) = P0 P1 /(P0 + (P1...

Sam is seeping into a room from the basement at a rate of $$\frac{1}{6} \times 10^6 \frac{\mathrm{pCi}}{\mathrm{hr}}$$ (pCi=picocuries). The room contains $$10^6$$ liters of air. (The rate was chosen so that the room reaches the EPA action level of $$4 \frac{pCi}{liter}$$ after $$24$$...

I realize that Δ(s) is the cross product of the matrix on the left, but how did the solutions manual get the matrix on the far right multiplied by R_1(s) and R_2(s)? I need those matrix values to do the rest of the problem. Any help is appreciated, thank you.

Greetings everyone. Can you help me please with solving this differential equation? \large \frac{dv}{dt} = a_g + \alpha v^n where \Large a_g \alpha n are constants. Artelnatively with specific n as n = 1, 2. I have no idea what to do... Thank you very much

Homework Statement If y is the solution of the initial value problem y'(t) + y(t)/t = 1/t4 y(2)=1 What is y(3) Homework Equations The Attempt at a Solution I u(t) = e∫1/t dt = eln t = t ∫[yt]' dt = t-4 dt yt = -1/3t3 + C Plugging in my initial value I solve for...

Take for example a system of differential equations: dx/dt=f(x,y) dy/dt=g(x,y) If I plot the surfaces for f(x,y) and g(x,y) and find their intersections,what does this symbolize in terms of the differential equations? I'm thinking equilibrium points(??) Can one go further and find the...

Hi, I'm having trouble understanding what to do when a First order equation has an inequality at the end of it. For example : sqrt(y-x^2y)*dy/dx = -xy where -1<x<1 I've solved the differential equation with y = 1/4(2C*sqrt(1-x^2) + C^2 -x^2 +1) where C is a constant. What do I do with...

Homework Statement The function satisfies the differential equation f''(x) = xf(x) and has boundary conditions f(0) = 1 and f'(0) = 1 Use Frobenius method to solve for f(x) with a taylor expansion of f(x) up to the quartic term a4x4 Homework Equations f(x) = a0 + a1x + a2x2 + a3x3 + a4x4...

Homework Statement Find the largest open rectangle in the ty-plane that contains the initial value point and satisfies the following theorem: Let R be the open rectangle defined by a<t<b, α<y<β. Let f(t,y) be a function of two variables defined on R where f(t,y) and the partial derivative...

Homework Statement The radioactive decay of a substance is proportional to the present amount of substance at any time t. If there was 15 grams at t=0 hours and 10 grams at t=3 hours. Set up the differential equation that models this decay and use the method of separation of variables to solve...

Homework Statement A psychology class is studying memory. Several objects are uncovered to view for a given amount of minutes and then covered again. At most 150 objects can be viewed and remembered. The class found that after 10 minutes the average student could remember 25 objects. The...

While studying the derivation of the normal modes of oscillation of a liquid sphere in the paper "Nonradial oscillations of stars" by Pekeris (1938), which can be found here, on page 193 and 194 two coupled second order differential equations in two variables are merged into one fourth order...

Homework Statement If y satisfies the differential equation: ty'(t) + tln(t)y(t) = 0 and y(1) = 3 then y(1/2) = ? I have attached an image of the question with the possible solutions: Homework Equations The Attempt at a Solution Initially I tried plugging in t=1 and...

mathematics - Q 8 -- Forming Differential Equations

Homework Statement Here is the whole problem. Homework Equations Not sure The Attempt at a Solution As you can see I got the first part. I solved the equation at part a.) for A(c) and plugged it into the D.E. and then solved for B(c). I need help on how to do the next part. How...

Homework Statement Determine the solution and limiting factor (t+1)y' + y = 6 y(1) = -2Homework Equations The Attempt at a Solution So I started off by isolating y' y' + y/(t+1) = 6(t+1) Then I found u(t) u(t) = e∫ t+1 dt = et2/2 +t y' =(et2/2 +t) = y(et2/2 +t) = 6(et2/2 +t)/(t+1)...

Homework Statement Use the method for Homogeneous Equations to slove (xy + y^2) dx - x^2 dy = 0 Homework Equations The Attempt at a Solution I attempted to get dx/dy on one side and substitute but could not get farther than this dx/dy = x^2/(xy + y^2)

Homework Statement I'm having problems with some differential equations, just need to know where I'm going wrong. Homework Equations The Attempt at a Solution a) mv\stackrel{dv}{dx}=F(x) mvdv=F(x)dx m∫vdv=∫F(x)dx v^2=vv^{2}_{0}+\stackrel{2}{m}∫F(x)dx...

Homework Statement Which of the following differential equations are linear? Put the linear differential equations in proper linear form a) t2dy/dt -et = ty b) dy/dt + ytan(t) -ety(2)=0 Essentially, I'm struggling with basic algebra. I've had no luck moving the dependent variable, y...

Author: Vladimir I. Arnold, R. Cooke (Translator) Title: Ordinary Differential Equations Amazon Link: https://www.amazon.com/dp/3540345639/?tag=pfamazon01-20 Prerequisities: Introductory Calculus Level: Adanced Undergraduate or Graduate Table of Contents: Basic Concepts Phase Spaces...

I am taking my first differential equations course. I am using the textbook by Edwards and Penney. My problem with this book is that it holds your hand a little bit too much. I don't like that I have to read huge amounts of explanation just to get a small amount of information. Does anyone know...

Homework Statement A falling body of mass m, encounters air resistance proportional to its instantaneous velocity, v. Use Newton's second law to find the DE for the velocity, v at time, t. Homework Equations I've been reading this section quite a bit and am still not getting it! I'd...

Author: David Bleecker (Author), George Csordas (Author) Title: Basic Partial Differential Equations Amazon Link: https://www.amazon.com/dp/1571460365/?tag=pfamazon01-20 Prerequisities: Table of Contents: Preface Review and Introduction A Review of Ordinary Differential Equations...

Homework Statement Solve: dP/dt + 2tP = P + 4t - 2 The Attempt at a Solution I've done a couple of these but I'm not sure how to start with this one... First I have to put it in standard form right? dP/dt + P(2t - 1) = 4t - 2 Then obtain the integrating factor by...

I am trying to figure out what I am doing. Forgive me, I’m not very sharp when it comes to differential equations… or even a useful working knowledge of calculus. I understand the concepts but if I can’t figure out how to type it into my TI-89 or get Wolfram alpha to do it… I’m kind of stuck and...

Homework Statement Show that sines and cosines are the solutions of the differential equation f''(x) = (-σ^2)f(x) What if a boundary condition is included that g(0) = 0? Homework Equations f''(x) = (-σ^2)f(x) The Attempt at a Solution Plugging in sin(σx) and cos(σx) yields an...

Homework Statement y = 2xy' + y(y')2; y2 = C1 (x + C1 /4) 2. The attempt at a solution I thought that I could take the first equation and set it equal to zero. But the C1 in the second equation is throwing me off. Am I supposed to set the second equal to C1?

Hi I am a physics major and I am trying to double major in math,I will be taking a differential equations course for pure math students this semester. I need advice on a good textbook in Differential Equations for pure mathematicians that will build up a great intuition for proofs and will have...

Can anyone explain why we obtain the part where i put the red underline. I understand everything until then

I'm having some difficulties figuring out how to linearize second order differential equations for a double pendulum. I have an equation that is in the form of \theta_{1}''\normalsize = function [\theta_{1},\theta_{2},\theta_{1}',\theta_{2}'] (The original equation is found at...

(d4x)/(dt4) + (1/(1+t))*(d2)/(dt2) = x(t) Is this differential equation linear or non-linear? I don't understand the difference.

Homework Statement http://sphotos-d.ak.fbcdn.net/hphotos-ak-ash3/526007_3920535257917_1525052730_n.jpg Write down the differential equations of motion. (Step by step if you can)2. The attempt at a solution x"+(f/m)x'+3(k/m)x=0 or x"+σx'+ω^2x=0 where σ=f/m and ω=sqrt(3k/m) Thanks in advance.

Can anyone recommend a good differential equations and linear algebra book? The books that I've read so far are Linear algebra: https://www.amazon.com/dp/0030103479/?tag=pfamazon01-20 Differential Equations: https://www.amazon.com/dp/0534373887/?tag=pfamazon01-20 I was able to get an...