 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-1/6b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

For drift

A_{i} (x)

b_{ij}

\frac{\partial P}{\partial t} = - \frac{\partial}{\partial x _{i}} (A_{i} P) + \frac{1}{2} \frac{\partial ^{2}}{\partial x _{i} \partial x _{j}} (b_{ij} P) .

Here

A_{1} = - x_{1} + x_{2}, A_{2} = - 2 x_{1} - x_{2}, b = I,

\frac{\partial P}{\partial t} = \frac{\partial}{\partial x _{1}} [(x_{1} - x_{2}) P] + \frac{\partial}{\partial x _{2}} [(2 x_{1} + x_{2}) P] + \frac{1}{2} (\frac{\partial ^{2} P}{\partial x _{1}^{2}} + \frac{\partial ^{2} P}{\partial x _{2}^{2}}) .

 New to topics? Read the docs here!