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CSIR NET December 2024 · Part C (4.75 Marks)ODE, PDE & Applied Mathematics#the-sign-of-the-discriminant-is-what-is-preserved

Consider the partial differential equation 4(∂2u/∂x2)+6(∂2u/∂x∂y)+3(∂2u/∂y2)=04(\partial^{2}u/\partial{}x^{2}) + 6(\partial^{2}u/\partial{}x\partial{}y) + 3(\partial^{2}u/\partial{}y^{2}) = 0. Which of the following partial differential equations can be obtained by a change of independent variables given by (ξ,η)(\xi, \eta)ᵗ = A(x, y)ᵗ for some 2 × 2 invertible matrix A with real entries?

Multi-select · full marks only for the exact set · Partial Differential Equations

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