What is a solution to the differential equation $y'=-9x^2y^2$ ?

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Answer 1 · 2016-07-31T15:48:28

$y =1/ (3 x^3 +C)$

$y'=-9x^2y^2$

this is separable

$1/y^2 y'=-9x^2$

$int \ 1/y^2 y' \ dx=int \ -9x^2 \ dx$

$int \ 1/y^2 \ dy=-9 int \ x^2 \ dx$

$- 1/y =-3 x^3 +C$

$1/y = 3 x^3 +C$

$y =1/ (3 x^3 +C)$

What is a solution to the differential equation y'=-9x^2y^2y'=-9x^2y^2?