 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-2/17/b/i/solution

Yes. The differential operator

L = 2 y \partial_{x} - x \partial_{y}

is linear, even though its coefficients depend on position. For constants

A, B

L (A u_{1} + B u_{2}) = A L u_{1} + B L u_{2} .

If each homogeneous right-hand side is zero, so is their combination. Hence the superposition principle holds.

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