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 $y$ :

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

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

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