Question #3d111

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Answer 1 · 2017-02-05T02:02:04

#y(x) = root(3)((3x^4)/2 +C)#

This is a separable differential equation, so we can solve it by separating the variables on the two sides and then integrating:

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

#y^2dy = 2x^3dx#

#int y^2dy = 2int x^3dx#

These are standard integrals we can solve using the power rule:

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

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

and finally:

#y = root(3)((3x^4)/2 +C)#