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

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

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

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

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

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

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