Odd that you know it's a Bernoulli equation, yet seem to have no technique for solving such a well-known form.
y = ±1/?(cx^2-6x^3)
If you have not studied them, try here:
http://tutorial.math.lamar.edu/Classes/DE/Bernoulli.aspx
dy/dx+(1/x)y=3x^2y^3 find the solution using Bernoulli equation
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