 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/14/a/iii/solution

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\partial_{x} = \partial_{ξ} + \partial_{η}

u_{xx} = U_{ξξ} + 2 U_{ξ η} + U_{ηη} .

Here and in the next part the second partial derivatives are understood with the usual smoothness required for this partial differential equation.

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