Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 54

The Bernoulli ODE is named after Jacob Bernoulli. It is special in the sense that it is a non-linear equation having an exact solution:

(3.8)

In the cases and and when P and Q are constants, this equation is linear, and an exact solution can then be found. We reduce Equation (3.8) to a linear one by the substitution to produce the following linear ODE:

(3.9)