I am trying to get sage to solve for the intersection of two Gaussian distributions. Using the solve command does not yield an answer unless I more the exponential terms to both sides. I am trying to solve for the variable y. here is the code:
eqn =1/(sqrt(2*pi*N))*exp(-y^2/(2*N)) == 1/(sqrt(2*pi*(N+P)))*exp(-y^2/(2*(N+P)))
solve(eqn, y)
this results in:
[e^(1/2*y^2/(N + P)) == sqrt(pi*N)*e^(1/2*y^2/N)/sqrt(pi*N + pi*P)]
Which doesn't solve for y.
However If before calling solve I divide both sides by one of the exponentials, the solve functions works as expected.
solve(eqn/exp(-y^2/(2*N)), y)
which yields:
[y == -sqrt(2*N*log(sqrt(pi*N + pi*P)/sqrt(pi*N)) + 2*N^2*log(sqrt(pi*N
+ pi*P)/sqrt(pi*N))/P), y == sqrt(2*N*log(sqrt(pi*N + pi*P)/sqrt(pi*N))
+ 2*N^2*log(sqrt(pi*N + pi*P)/sqrt(pi*N))/P)]
Is this a bug? or am I missing something?
