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

1 Answer
Sep 16, 2016

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

Explanation:

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)