I want to use DSolve
to solve a differential equation while imposing a boundary condition and normalization.
How can I do that?
Let's take for example a simple heat-equation: $y''[x]=a y[x]$. Easy to solve:
DSolve[y''[x] == a y[x], y[x], x]
I can also impose a no-flux condition at position L
, $\nabla \rho|_L=0$
DSolve[{y''[x] == a y[x], y'[L] == 0}, y[x], x]
but I cannot (or don't know how to) impose a normalization condition, $\int_0^L\rho(x)dx=1$
DSolve[{y''[x] == a y[x], y'[L] == 0, Integrate[y[x], {x, 0, L}] == 1},
When I evaluate the above expression, I obtain the following error:
There are fewer dependent variables than equations, so the system is overdetermined"
But that is something I can do by hand. What is the problem? Is it a bug or am I misunderstanding something?