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QUESTION
Consider the constants A, B, C and the function f(x, y) = Ax^2 + Bxy + Cy^2.
Consider the constants A, B, C and the function
f(x, y) = Ax^2 + Bxy + Cy^2.
Show that the only choice of coefficients A, B, C giving ∂^2f/∂x^2+∂^2f/∂y^2= 2,
are A=1-s2
B=s1
C=s2
where s1, s2 are arbitrary.
f(x, y) = Ax^2 + Bxy + Cy^2. ∂f/∂x = 2Ax + By∂f/∂y= Bx + 2Cy ∂^2f/∂x^2 = 2A∂^2f/∂y^2 = 2C ∂^2f/∂x^2+∂^2f/∂y^2 = 2A + 2C = 2Therefore A + C = 1Taking B = s1 and C = s2 (...