Theorem: dI/dx + mu I = 0 for I(x) = I_0 e^{-mu x} (Beer-Lambert ODE residual)

Theorem (Beer-Lambert-ODE canonical): for I(x) = I_0 exp(-mu x), differentiation gives dI/dx = -mu I_0 exp(-mu x) = -mu I, hence dI/dx + mu I = 0 identically as a first-order linear ODE. Canonical sympy pins: mu, I0, x = sp.symbols('mu I0…