Verify that the conclusion of Clairaut's theorem holds, that is, Uxy = Uyx" u = x5y8 - y5 With u = x5y8y5, we have the following. 5x4 U xy = Uyx = "y=40x4₂7 40x¹y7 = 8x5y7 - 5y4 × Since u xy X = U Clairaut's theorem holds for u = x5y8-y5. 'yx'

Find x1, x2, x3 with gauss jordan

ӘР ӘР Find and when x = 0, y = 2 if P = √u² + v2 + w², u = xey, v = ye*, and дх ду W = exy.

ts) Find two linearly independent solutions of 2x²y" - xy + (2x + 1)y=0, x > 0 of the form Y₁ = x¹(1+ a₁ + a₂c² + a3x³ + ...) Y₂ = x²(1 + b₁c + b₂x² + b3x³ + ...) where T1 T2. Enter T1 T2 a1 = a₂ = a3 = b₁ b₂ TE b3 N - || || || || =