Diff eq Definition and 271 Threads

In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.
Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

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  1. S

    My final Diff Eq question for now

    Here u(x,t) refers to D'ALembert's solution for the one dimensional wave. L represnets the legnth of the string and c, the speed of the wave. Find u(3/4,2) where l=c=1 f(x) = x(1-x), g(x) = x^2 (1-x) Ok i know that from earlier that i ahve to extend g as an even periodic function over this...
  2. infraray

    How Do You Solve the Differential Equation for Particle Motion with F=kvx?

    I'm given F=kvx. I need to find x(t), k is a positive constant, and the particle passes thru the origin with speed Vo at time t=0. I start by rewriting the formula as such: dv/dt=k*dx/dt*x I am confused now though because I now have dv,dt, and dx. I assume I need to get everything in...
  3. G

    MATLAB MATLAB Diff EQ Help: Solve ODE for b=0, b=2, b=8, b=10 & k(t)=16e^-LT

    I am new to MATLAB and need help with a problem. we have tried several different methods and each time can't make sense of what is going on wrong " A mass spring motion is governed by the ordinary differential equation m(dx^2/dt^2) + b(dx/dt) + kx=F(t) , where m is the mass, b is the...
  4. V

    Series Diff EQ problem: (3 - x^2) y'' - (3x) y' - y = 0

    The problem (#11, 5.2, boyce diprima): (3\,-\,x^2)\,y''\,-\,(3\,x)\,y'\,-\,y\,=\,0 I got the recursion formula as: a_{n\,+\,2}\,=\,\frac{(n\,+\,1)}{3\,(n\,+\,2)}\,a_n Which give the following results: \begin{flalign*} a_2& = \frac{1}{6}\,a_n\,x^2& a_3& = \frac{2}{9}\,a_n\,x^3&...
  5. P

    Need help finding solutions to Diff eq

    Hi, I need help to solve two differential equation: 1. Find all solutions to the differential equation 3y' - 2y = 1 - x 2. Find the solution to 2y' + 3y = 4 when y(2) = 0 I would be happy if anyone could explain the general rule to solve these two equations, because the book I use only...
  6. W

    Can Constant Velocity be Solved with Separable ODEs?

    This is probably too hard to be the first problem I try for diff eq. I'm trying to learn this stuff. Question, what's the difference between a homogenous and nonhomogenous one? What problem does this pose in solving the problem? I want to try this one (jacked from Naeem's post, but I posted...
  7. K

    Am I setting this diff eq up correctly?

    The problem: A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved. Brine containing .5 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well mixed solution is then pumped out at a rate of 4 gal/min. Find the number of...
  8. K

    Finding Roots of Diff EQ: c1 & c2?

    When you are trying to determine the general solution of a homogeneous linear ordinary differential equation, after you find the roots, how do you decide which goes with c1 and which goes with c2? example: y''-3y'+2y=0 Factoring the auxiliary equation m^2-3m+2=0=(m-1)(m-2) is...
  9. B

    How Do I Solve This Initial Value Problem Using a Given Solution Function?

    I'm hacking at this particular linear system: dY/dt = [1, -1; 1, 3] Y I've already found myself a solution using the following function: Y(t) = [ te^(2t), -(t+1)e^(2t) ] That was fun, actually, once I figured out what the hell I was doing. Here's my question: the next part of...
  10. F

    Diff Eq and the Dirac Delta(impulse) function.

    Ok, I was given: Solve the following using superposition: \ddot{x}+2\dot{x}+4x=\delta(t) bounded by \dot{x}=0, x(0)=0 I solved the Homo eqn and got the following: x(t)=e^{-t}(\cos (\sqrt{3}t)+\frac{\sqrt{3}}{3}\sin ({\sqrt{3}t)) I also know that : \ddot{x}+2\dot{x}+4x=u(t)...
  11. K

    How Does Substitution Work in Solving Homogeneous Differential Equations?

    The book only has one example of this and it's really confusing me. (x^2+y^2)dx+(x^2-xy)dy=0 I can see that it's homogeneous of degree 2 They then let y = ux From there they state that dy = udx+xdu (I'm not sure where this is coming from, but can just accept it on faith if I have to)...
  12. K

    Is Multiplying Both Sides by -1 Necessary for Solving Differential Equations?

    I'm pretty sure I know the answer to this, just want to double check. For the problems that I'm currently working on, we are just solving the problems for an unknown constant C. I just finished one were I came up with \frac{x^2}{2}-y^2cos x-xy^3=C The book shows the solution as...
  13. F

    Solving a Second Order Differential Equation with Circuit Components

    dv(t)/dt + 200v(t) = 10 cos(100t) v(0)=0 find v(t) i know v(t) is going to have an exponential and sinusoid component i also know that 200*ke^-st=-ske^-st so, s = -200. i don't know how to find k. i also can't figure out how the sinusoid part is going to be. the equations from my...
  14. K

    Calc III or Diff Eq: Which to Take First?

    I am considering taking 1 or the other and possibly both next semester. Is there any advantage to taking one of them first, will taking calc III help me with diff eq or vice versa?
  15. K

    Good Diff EQ Book? EE Major Suggestions

    Can somone recommend a good diff EQ book? Something that would be good for learning it on your own. I'm majoring in electrical engineering, not mathmatics, if that makes any difference to your suggestions. Thanks.
  16. F

    Classifying a Diff Eq: Linear vs. Non-Linear Techniques

    x(dy/dx) = y*e^(x/y) - x its either separable, linear, homogeneous, bernoulli or exact. only thing i can figure is that its linear. how do i break it down to figure it out? the e^x/y is what's throwing me off.
  17. T

    Having difficulty setting up a Diff Eq for this situation

    Suppose the population of mosquitos in a certain area increases at a rate proportional to the current population... in the absense of other factors, the population doubles each week. There are 200,000 mosquitos in the area initially, and predators (birds, etc) eat 20,000 mosquitos /day...
  18. Loren Booda

    How Does Maxima Solve the Differential Equation r=Kt/((dr/dt)²-c²)?

    Please solve r=Kt/((dr/dt)2-c2) where r and t are variables, and K and c are constants.
  19. R

    Nonhomogeneous System of Linear Differential Equations

    Nonhomogeneous system of lineair differential equations This is a given system: D\vec{y} = A\vec{y} + \vec{b} With A=\left\begin{array}{ccc}1&1&1\\0&2&1\\0&0&3\end{array}\right And \vec{b}=\left\begin{array}{c}e^4^t\\0\\0\end{array}\right We find \vec{y}_H = Y(t) \cdot \vec{c} With...
  20. P

    Uncovering the Practical Applications of Differential Equations

    What is the true use of Differential Equations?
  21. M

    A diff Eq on strings, check out the math.

    Check my math! I've derived a differential equation for strings starting from Stokes Theorems to show that energy is conserved along the world-sheet. These diff eq's involve connection coefficients. And I'm not really sure what it all meants yet. I would appreciate it if some who are more...
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