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Differentiating both sides of (1) with respect to x.

Or, d / dx (x ^3) +3 d /dx (x^2 y) -2 d/dx (y^3) = d/dx (5)

Or, 3x^2 +3 {x^2 dy/dx + y d/dx(x^2)} – 2 *3y^2 dy/dx =0

Or, 3 x^2+3 (x^2 dy/dx + y * 2x) – 6 y^2 dy/dx = 0

Or, 3 x^2+3 x^2 dy/dx +6 x y- 6 y^2 dy/dx=0

Or, -3 dy/dx (2 y^2-x^2) + 3 x (x + 2 y)= 0

Or, -3 dy/dx (2 y^2-x^2) = -3 x (x + 2 y)

Or, dy/dx = 3 x (x + 2 y)/ 3 (2 y^2-x^2)

Therefore, dy/dx = x (x + 2 y)/ (2 y^2-x^2)

d / dx (x) + d /dx (y) = d/dx (1)

or, 1 + dy/dx = 0

or, dy/dx = -1

Therefore dy / dx = -1