Well actually my question is because I am trying to solve the homogeneous part of a 2nd order inhomogeneous differential equation with variable coefficient.
Could you give some hints on the Fourier expansion, or any good reference to that?
My main goal is to solve the differential equation...
Homework Statement
I need to work on a differential equation.
\frac{d^2T}{dx^2} - (m+n\ sin(kx))\ T = 0
Homework Equations
Is my work correct?
The Attempt at a Solution
\frac{d^2T}{dx^2} - (m+n\ sin(kx))\ T = 0
\frac{d}{dx}\left(\frac{dT}{dx} \right) = (m+n\ sin(kx))\ T
\int...
Homework Statement
Find the the T(x). See attachment. The top, bottom as well as the left side are adiabatic. The fluid temperature on the side of convective heat transfer is a function of x. The dimension for the width is W.
Homework Equations
How to find T(x)
The Attempt at a...
well it starts with a differential equation, I am using the method from a calculus book written by Adams. My idea was to calculate that "unsolvable" integral part with matlab.
Thanks for the tips,
Out of curiosity, how did you get a solution as a series function?
this is the original equation:
e^{-a cos wt} \ T(t) = m \int e^{-a cos wt} dt + p \int sin wt \ e^{-a cos wt}
I want to have solution for T(t)
e^{-a cos wt} \ T(t) = m \int e^{-a cos wt} dt + p e^{-a cos wt}
The initial condition is:
T(t=0) = T_0
I really do not know how did you get that..
Actually, I got this integral when I try to solve a 1st order inhomogeneous non-linear differential equation with variable coefficients..
So.. I am stuck with that integration. Suppose that your solution is correct, I really do not know how to...
Homework Statement
I need to integrate the following function:
y = \int e^{-\frac{n}{\omega}cos \omega t} dt
Homework Equations
How should I solve this? Will this lead me to Bessel function?
2. My attempt
a=\frac{n}{\omega}
u=-a cos (\omega t)
du = a\omega sin...
Dear all, I have difficulty in solving this problem (see the figure in attached thumbnails)
I have a rectangular shape with length/height of L and the thickness/width of \delta
Within the rectangular area, a heat conduction occurred. I would like to determine the temperature profile within the...