What is a general solution to the differential equation #dy/dx=x^3/y^2#?

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Answer 1 · 2016-09-16T03:33:28

#y=root3((3x^4)/4+C)#

Treat #dy/dx# like a fraction to move the #y# terms to one side of the equation and the #x# terms to the other:

#dy/dx=x^3/y^2" "=>" "y^2dy=x^3dx#

Integrate both sides:

#=>" "inty^2dy=intx^3dx#

Using the typical integration power rule:

#=>" "y^3/3=x^4/4+C#

Solving for #y#:

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

#=>" "y=root3((3x^4)/4+C)#