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...
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...
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)...
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.
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...
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...
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...
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...
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...
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##.
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...
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
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...
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 =...