Differential equations Definition and 999 Threads

Hi, I'm not a bright programmer , but I have to solve the fallowing equations: ##\frac{df}{dt} = \alpha f -\beta f + \theta g - (f+h)f## ##\frac{dg}{dt} = \psi f- \phi g## ##\frac{dh}{dt} = \xi f+ \mu h -\tau h + \epsilon w- (f+h)h## ##\frac{dw}{dt} = \nu h - \chi h## Where ##f(t)## ...

Hi, So, I'm a programmer with a deep interest in simulations and mechanics and I'm currently trying to delve into a bit of fluid simulation. To set the scene, I'm completely new to this field and my searches so far have yielded such things as 'Stokes-Navier equations' which no doubt sound...

Hello all, I've got one more semester before I earn my physics MS, and I have space for one or two extra courses. I am going into oceanography, and I would like to have a strong foundation in math in order to understand the theory I'll encounter as well as possible. Lots of physical...

I have determined the solution to a nonlinear first order ordinary differential equation but am struggling to rearrange the result, I have that $$\\ln(R)+\frac{mR^{n-1}}{n-1}=\bar{w}_{\infty}\xi+C.$$ How would I rearrange this equation for $$R$$?

Homework Statement Suppose that ##s \to A(s) \subset \mathbb{M}_{33}(\mathbb{R})## is smooth and that ##A(s)## is antisymmetric for all ##s##. If ##Q_0 \in SO(3)##, show that the unique solution (which you may assume exists) to $$\dot{Q}(s) = A(s)Q(s), \quad Q(0) = Q_0$$ satisfies ##Q(s) \in...

Q1. x2dy/dx + xy = x2sinx I believe it is a separable equation (first order linear) First step is to rewrite into standard form; dy/dx + (xy)/x2 = (x2sin(x))/x2 Then to calculate the integrating factor I(x); I(x) = e|(xy)/x2dx = eylnx = elnxy = xy Then i need to multiply both sides of...

Ok, for my differential equations class we are using a textbook called "An Introduction To Differential Equations and Their Applications" by Stanley Farlow. The book can be found here: https://www.amazon.com/dp/048644595X/?tag=pfamazon01-20 and I must say that I 100% agree with the assessment...

I am quite embarrassed to ask this question, as I know i have lost track of the concept here, but Ill nevertheless ask it. I was going through Mathematical methods for physicists (pg 333), and there was an example: "Solve $$y'+(1+\frac{y}{x}) = 0$$" My problem is, (a) when you put the...

Hello all,As an exercise my research mentor assigned me to solve the following set of equations for the constants a, b, and c at the bottom. The function f(r) should be a basis function for a cylindrical geometry with boundary conditions such that the value of J is 0 at the ends of the cylinder...

Is the derivative of a function a differential equation? I guess it would be because it involves a derivative, right? Would the solution to the equation just be the original function? Is solving a differential equation just another way of integrating? Like with finding solutions of separable...

Homework Statement Solve the following ordinary differential equations, where ##\alpha##, ##\beta##, and ##\lambda## are constants. \frac {dy}{dx} + \beta y = 0 \frac {dy}{dx} + \beta y + \alpha = 0 \frac {d^2y}{dx^2} - \lambda^2 y = 0 \frac {d^2y}{dx^2} + \lambda^2 y = 0 \frac...

from the attachment a) when I put dw/dt = 0 I get something like e^(b/a) is this correct?

Homework Statement A college student wants to start a new savings account with an initial balance of $0. He plans to save money at a continuous rate of $700 per month. Additionally, every month he plans to increase this rate by $7. (Such that for example in month 3 he is saving at rate $721...

I've been given this: x''+ x = 4δ(t-2π) The question asks: With initial conditions of x(0) = 1 and x'(0) = 0, find x(t) using Laplace transforms. I can easily get it to this: 4(sin(t-2π)u(t-2π)) But the question says "express your final solution without use of the unit step function". This is...

(r^2) (dT/dr)+B*r*T=T^2, with initial condition dT/dr |r=0 =0 where B is a constant I've gotten it to this: dT/dr = -BT/r + T2 / r2 by dividing everything by r2, then I substitute using λ= T/r which gives: r * dλ/dr + lambda = -B * (λ) + λ^2 I don't know how to separate...

I had a brief question regarding SDEs. Typically, I've seen models like the Ornstein-Uhlenbeck process that generally revert back to the mean over time. However, I've been trying to find a stochastic differential equation/process that avoids the mean, such as a sharp increase followed by a sharp...

(a) all circles tangent to x-axis?? with answer on the book [1+(y^{2})^2]^3=[yy''+1+(y')^2]^2 (b) all circles with fixed radius r and tangent to x-axis?? Thanks a bunch!

What is the vector space under consideration when we say that a linear differential equation is of the form Dy=f where the differential operator D is a linear operator? What is its underlying field? Also, is the Fourier series just an expansion (for a subspace of this vector space) in the...

Hi! My task is to solve this system: $$\frac{\mathrm{d} x}{\mathrm{d} t}=-x+y-2z$$ $$\frac{\mathrm{d} y}{\mathrm{d} t}=4x+y$$ $$\frac{\mathrm{d} z}{\mathrm{d} t}=2x+y-z$$ My first equation (1) is $$\frac{\mathrm{d} y}{\mathrm{d} t}=4x+y$$. Derivative of (1) is $$\frac{\mathrm{d} }{\mathrm{d}...

The 3 nonlinear differential equations are as follows \begin{equation} \epsilon \frac{dc}{dt}=\alpha I + \ c (-K_F - K_D-K_N s-K_P(1-q)), \nonumber \end{equation} \begin{equation} \frac{ds}{dt}= \lambda_b P_C \ \epsilon \ c (1-s)- \lambda_r (1-q) \ s, \nonumber \end{equation}...

Can someone please recommend me a good textbook for Differential Equations that has lots of practice problems and less theoretical problems? Please tell me the name of the textbook, edition, and author. Thanks.

I want to show, in a talk, how to build the Predator-Prey (Lotka Volterra) model. It starts off with the "Population Law of Mass Action" i.e. "At time t the rate of change of one population due to interaction with another is proportional to the product of the two populations at that time t"...

I thought I got this problem wrong, but I think I have it right now. It turned out that when I was taking the derivative of e^xy2with respect to y, I forgot that you're supposed to multiply by 2xy (the derivative of xy2), not just x. Homework Statement (y2* e^xy2 + 4x3 dx + (2xy * e^xy2 -...

Homework Statement x*e^(y/x) + y dx = xdy, y(1) = 0 Homework Equations The Attempt at a Solution To solve, I divide everything by x dx to put everything in terms of v. e^v + v = dy/dx dy/dx = x dv/dx + v e^v + v = x dv/dx + v e^v = x dv/dx e^v / dv = x/dx Flip both sides. e^-v dv =...

I'm a little rusty with partial fractions, and I can't seem to find my error once I get up to that point. Homework Statement dy/dx = (y^2 - 1) / x Homework Equations The Attempt at a Solution Cross-mutliply x dy = (y^2 - 1) dx Divide by the appropriate terms dy / (y^2...

#1 Which of the following FUNCTIONS are SOLUTIONS (meaning PLURAL) of the differential equation $y''+y=sin(x)$? a. $y=sin(x)$ b. $y=cos(x)$ c. $y=\frac{1}{2}xsin(x)$ d. $y=\frac{-1}{2}xcos(x)$#2 Suppose you have just poured a cup of freshly brewed coffee with temperature $95^oC$ in a room where...

I hope I am putting this in the right thread. It seemed to be the most appropriate one! So, I have two choices. I can take both MA 227(Calculus III) and MA 252 (differential equations) or take both EGR 254 and EGR 254. Which do you think would be the easiest option? I am an electrical...

did i do these two questions right? #1 $y'=xe^{- \sin\left({x}\right)}-y \cos\left({x}\right)$ $y'+y \cos\left({x}\right) = xe^{-\sin\left({x}\right)}$$I(x)=e^{\int \ \cos\left({x}\right)dx}$ $\int \...

Is the course "Complex Variables with Applications" taken after Differential Equations? Is this course applied or pure math? Can someone recommend me a good textbook for this course?

Hi, I am taking (ordinary) differential equations as a summer course and we are studying from a horrid textbook, in my opinion. Just curious if anyone might be able to suggest what is considered to be the "standard" introductory text on ODE. While I'm certainly interested in PDE, I don't...

Sketch a direction field for the differential equation. Then use it to sketch three solution curves. $y'=x-y+1$ I really need help drawing this, I'm super confused. :confused:

Hi, Are there any numerical techniques I can use to solve differential equations with periodic boundary conditions? I know of several techniques for other kinds of boundary conditions (such as Runge-Kutta method, Euler method etc.), but I am interested in knowing how to numerially solve...

So I am going to take some Math test. For the DEs portion, they recommend me to read the first ten chapters of Hirsch's "Differential Equations, Dynamical Systems, and Linear Algebra. First Edition" However, I got the third edition which the book title and contents are a little different. It is...

Hello everyone, I am currently entering my second year of college in the fall, and will begin Calc 2. My questions involves whether or not it is a good idea to take Calc 3 and differential equations the same semester. The community college I'm attending does not offer linear algebra, so I can...

Homework Statement Find the differential equation of ln y = ax^2 + bx + c by eliminating the arbitrary constants a, b and c. Homework Equations Wrosnkian determinant. The Attempt at a Solution I've solved a similar problem (y=ax^2+bx+c --> y'''=0), but couldn't do the same with...

Hello, I am going into my first semester at university in the fall and I have already completed Calc I and II and linear algebra and I am finishing up Calc III over the summer. So I was talking to the chair of the EE department at my university and he recommended I take ODEs my first...

I mean is it possible? would it be a problem?

I've attached a picture of the problem statement, figure, and of my work so far. I'm trying to use mesh currents and then differentiate it, but I really have no idea if I'm on the right track. Also, I don't understand why i1 isn't just V/R (The physical current is the mesh current for R1...

I want to find geodesics on 2-dimensional Anti de-Sitter space. According to http://www.aei.mpg.de/~gielen/ads.pdf I can write the metric of this as ds^2 = - \cosh^2{r} dt^2 + dr^2 Now, we know the geodesic equation is \frac{d^2 x^\mu}{d \tau^2} + \Gamma^\mu{}_{\nu \rho} \frac{d x^\nu}{d...

I've been reading Oksendal, and it's quite tedious. It want to see if my understanding of the motivation and process is correct. 1) Differential equations that have random variables need special techniques to be solved 2) Ito and Stratonovich extended calculus to apply to random...

Homework Statement Eliminate the arbitrary constants of the equation: ax2 + bx + cHomework Equations (Concept) According to my instructor, having n arbitrary constants makes an nth-order differential equation.The Attempt at a Solution I tried to differentiate 'til I get a third derivative so I...

This semester I'm a bit stuck with classes to progress my Electrical Engineering major (having going into it so late), so the only class I can take to progress is a physics course about electricity and the likes. I need at least a three unit class in order to get at least half time so I won't...

I apologize for the informal and un-rigourous question. I have heard, in passing, that doing Galois Theory over Lie Groups instead of discrete groups is connected to solutions of differential equations instead of algebraic equations. First of all, is this correct? If so, what is this...

Any books that are easy to understand on partial differential equations? I just came back from barnes and noble. I briefly looked at the book on partial differential equations, but it is confusing for me because it jumps to topics about partial differentiation that I didn't learn. The only...

say we have gone through the steps and have... ##(\lambda - 2)^{2}(\lambda ^{2}-9) = 0## which we can write as... ##(\lambda - 2)(\lambda - 2)(\lambda ^{2}-9) = 0## we have value for lambda of 2, 2, 3, -3 because we have a repeated root. now, say we have ##(\lambda^{2} -...

What book can I use to learn methods of solutions for differential equations not covered in this textbook...

Does MATLAB solve differential equations?

dear all, I am working on a problem about the vibration of a piezoelectric ring with electrodes on the upper and lower surface. the coordinate system is cylinder coordinate system. the structure is shown below. This is an axisymmetry problem. the polarization of the piezoelectric ring is...

I am going to quote an article below and there is a part I would like clarification.I do not understand why chaotic differential systems do not have an analytical solutions. In the simplest form,an equation such as this one [sin(x) + x - 0.5 = 0] does not have an analytical solution i.e it can...

System of PDEs--Heat Equation For Two Objects Hello everyone, Before is a system of partial differential equations; to be specific, it is this system: \frac{\partial U_A }{\partial t} = - \frac{k_B}{k_A} \alpha_A \left( \frac{\partial^2 U_B}{\partial x^2} + \frac{\partial^2 U_B}{\partial...