Hey Guys;
I'm solving PDE's with the use of Green's function where all the boundary conditions are homogeneous.
However, how do you solve ones in which we have non-homogeneous b.c's.
In case it helps, the particular PDE I'm looking at is:
y'' = -x^2
y(0) + y'(0) = 4, y'(1)= 2...
This all depends on the coordinate system that you choose. A good idea before starting a question is to set up your coordinate system such that it will make your solution simpler. Make sure that you be consistent though in your signs and it helps to draw a diagram to be reminded of your choice...
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Well looks like I made an error in my calculations: the integral turns out to be :
t =\frac{-m}{b} \frac{1}{b + c v} ln\frac{v}{1+\frac{c}{b}v}
And yes, using partial fractions will also solve this integral, and yes a ln function will turn out to be there.
Anyway, then the solution is...
An object is coasting on the horizontal axis, in the positive direction and is subject to a drag force f = -bv - cv^{2}.
Write down Newton's 2nd Law and solve for v using separation of variables.
So first I wrote out Newton's law as:
F= m(dv/dt) = -bv - cv^{2}
Solving the integral: dt =...