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)#