Question

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

Answer 1

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

Explanation:

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| ))`