What is the solution to the Differential Equation $4/y^3 dy/dx=1/x$ ?

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Answer 1 · 2017-06-12T14:44:16

$y = +-sqrt(2/(C-ln |x| ))$

We have:

$4/y^3 dy/dx=1/x$

This is a first Order Separable Differential Equation, we can just "separate the variables" to get

$int \ 4/y^3 \ dy=int \ 1/x \ dx$

And integrating gives us:

$4 \ y^(-2)/(-2) = ln |x| + C$

$:. -2/y^2 = ln |x| + C$

$:. y^2 = -2/(ln |x| + C)$

$:. y^2 = 2/(C-ln |x| )$

$:. y = +-sqrt(2/(C-ln |x| ))$

What is the solution to the Differential Equation 4/y^3 dy/dx=1/x4/y^3 dy/dx=1/x?