5x/y-2y/x^2

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Solution for 5x/y-2y/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

(5*x)/y-((2*y)/(x^2)) = 0

(5*x)/y-2*x^-2*y = 0

5*x*y^-1-2*x^-2*y = 0

x*y^-1*(5-2*x^-3*y^2) = 0

-2*x^-3*y^2 = -5 // : -2*y^2

x^-3 = -5/(-2*y^2)

-3 < 0

1/(x^3) = -5/(-2*y^2) // * x^3

1 = x^3*(-5/(-2*y^2)) // : -5/(-2*y^2)

(2*y^2)/5 = x^3

x^3 = (2*y^2)/5 // ^ 1/3

x = (2^(1/3)*y^(2/3))/(5^(1/3))

x/y = 0

x*y^-1 = 0 // : y^-1

x = 0

x in { 0} 

x = (2^(1/3)*y^(2/3))/(5^(1/3))

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