What is a solution to the differential equation #dy/dx=(x^2+2)/(4y^3)#?

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Answer 1 · 2016-07-18T15:04:32

#y = pm root4(x^3/3+2x + C) #

#dy/dx=(x^2+2)/(4y^3)#

this is separable

#4y^3 dy/dx=x^2+2#

#int \ 4y^3 dy/dx \ dx=int \ x^2+2 \ dx#

#int \ 4y^3 \ dy =int \ x^2+2 \ dx#

#y^4 = x^3/3+2x + C #

#y = pm root4(x^3/3+2x + C) #