# diff eq

1. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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 =...