diff eq

  1. L

    Green's functions (Fourier Series)

    In order to obtain equation (3), I think I have to do the Fourier transform in the x direction: \begin{equation} \tilde{G}(k,y,x_0,y_0) = \int_{- \infty}^{\infty} G(x,y,x_0,y_0) e^{-i k x} dx \end{equation} So I have: \begin{equation} -k ^2 \tilde{G}(k,y,x_0,y_0) + \frac{\partial^2...
  2. J

    I Quick question for Finding EOM with diff eq

    I have been going through my old books again, and found myself a little stuck. I am not entirely sure if this would be better in this one or diffy eq. The problem starts with having you find equation of motions when a= -bv, where b is constant and v = v(t) Using method of separable equations...
  3. JD_PM

    Dimensional analysis of an equation of motion

    1. Homework Statement The evolution of the density in a system of attractive spheres can be described by the following dynamic equation. $$\frac{\partial}{\partial t} \rho (r,t) = D_o [\nabla^2 \rho (r,t) + \beta \nabla \rho (r,t) \int dr' [\nabla V (|r-r'|)] \rho (r',t) g(r,r',t)]$$ a)...
  4. J

    A Can I linearize this equation?

    By using the laplace transform: $f(t)=sin(Φ(t))$ I want it in the form: F(S)/Φ(S) The purpose is to linearize it in order to put it into a larger transfer function, so far my only solution is to simplify it using taylor expansion.
  5. X

    A Need help solving Darboux equation

    I'm working on a personal math project and I'm running into this system of differential equations. I have seen references which state the solutions are in terms of Hermite modular elliptic functions, but I do not know what those functions are. All of the references I can find on this equation...
  6. PhysicsCollegeGirl

    Laplace transform (translation on the s-axis)

    1. Homework Statement L-1{[(2s-1)]/[(s^2)(s+1)^3]} 2. Homework Equations L{f(t)e^(at)}=F(s-a) 3. The Attempt at a Solution I have tried million ways but the different exponents in the denominator are throwing me off. The other problem is that I cannot use partial fractions, the homework...
  7. squelch

    Determining if Systems are Linear

    1. Homework Statement For each of the following, determine if the system is linear. If not, clearly state why not. (a) ##y''(t)+15y'(t)+sin(y(t)))=u(t)## (b) ##y''(t)-y'(t)+3y(t)=u'(t)+u(t)## (c) ##y'(t)=u(t)## and ##z'(t)=u(t)-z(t)-y(t)## 2. Homework Equations None 3. The Attempt at a...
  8. Steven Reichman

    Studying Why do I keep failing this in particular? (Differential Equations)

    Hello everyone. I'm an undergrad physics major with one semester left and I'm having some trouble. I took off 3 years to work on my depression and came back last spring to finish my senior year. Now, before I left I was struggling in all my classes due to my depression, but one was worse...
  9. F

    Ambiguity in the method applied for differential equations

    1. Homework Statement Why do we need two solutions to solve a 2nd order linear differential equation? lets consider a differential equation with equal roots for auxiliary equation. So the reasoning behind why cant we use y=Aen1x+Ben2x as its general solution is because since the roots are equal...
  10. X

    I Is this general solution correct?

    Question : General solution of dy/dt = -ay + b My solution : dy/dt = -a(y-b/a) (dy/dt)/(y-(b/a)) = -a Integrating both sides : ln | y-(b/a) | = -at + C e(-at+C) = y-(b/a) Ce(-at) = y-(b/a)
  11. M

    Need help solving a differential equation

    Are there any known analytical method to solve the equation $$ A\frac{d^2f(x)}{dx^2}+B\frac{df(x)}{dx}+Ce^{igx}f(x) = 0\hspace{1cm}? $$ All quantities appearing in that equation are complex except for ##g## and ##x##.
  12. ATY

    Elliptic partial differential equation

    Hey guys, so my professor told me to take a look at an equation, because he thinks that there is a mistake. We are basically talking about exercise 6.3 (on last image). The pictures will show you the text, so that you have all the information, that I have http://puu.sh/mrNDl/ec19cdff63.png...
  13. Just_some_guy

    General Solution from Particular Solution

    Just a question about the theory of solutions to differential equations? Given a second order differential equation and two particular solutions y1 and y2, what is the best way to find the general solution? i.e variation of parameters or something else
  14. T

    Friction constant minimizing the duration of vertical motion

    1. Homework Statement The mass of a car that acts on one wheel is 100 kg. The elasticity (spring) constant in the suspension system of that wheel is k = 10^4N/m. Design the strut (find the friction/resistance constant c) such that any vertical motion of the wheel (set up for example by going...
  15. S

    Learning Differential equations, week 2 level material

    1. Homework Statement Find the general solution to the equation. 2. Homework Equations (dy/dx) - y - e^3x=0 3. The Attempt at a Solution I rewrote this as dy/dx - y = e^3x This is a linear first order ODE, in the form dy/dx + P(x)y = f(x) P(x) = 1; f(x) = e^3x The integrating factor =...