What is a solution to the differential equation #dy/dx=(x+sinx)/(3y^2)#?

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Answer 1 · 2016-09-04T20:34:29

#y = root3 (x^2/2 - cos x +C)#

This is separable

#y' = (x + sin x)/(3y^2)#

#3y^2 \ y' = x + sin x#

#int 3y^2 \ y' \ dx = int x + sin x \ dx#

#int 3y^2 \ dy = int x + sin x \ dx#

#y^3 = x^2/2 - cos x +C#

#y = root3 (x^2/2 - cos x +C)#