If x^2 + y^2 = 10, show that y^3 d^2/dx^2 + 10 = 0 ?(Differentiation)

I've been trying over and over to try and solve this but I keep getting incorrect answers. Any help would be much appreciated :)

x² + y² = 10 ; Differentiate w.r.t x
2x + 2y(dy/dx) = 0
=> x + y(dy/dx) = 0 ..........(1) ; Differentiate again w. r. t. x
=> 1 + (dy/dx)(dy/dx) + y(d²y/dx²) = 0
=> 1 + (dy/dx)² + y(d²y/dx²) = 0
=> y(d²y/dx²) = - 1 - (dy/dx)² ....... (2)
From (1), (dy/dx) = - (x/y)
squaring both sides, (dy/dx)² = x²/y²
Substitute the value of (dy/dx)² in (2)
we get , y(d²y/dx²) = - 1 - (x²/y²)
=> y³(d²y/dx²) = - y² - x² = - (x² + y²) = - 10 (given, x² + y² = 10)
=> y³(d²y/dx²) + 10 = 0
=>