Find the general solution of the differential equations `x^5(dy)/(dx)=-y^5`

Explanation

Given,`x^(5)(dy)/(dx)=-y^(5)`
`implies (dy)/(y^(5))=-(dx)/(x^(5))`
`implies int(dy)/(y^(5))=-int(dx)/(x^(5))`
`impliesinty^(-5)dy=-intx^(-5)dx`
`implies(y^(-4))/(-4)=-(x^(-4))/((-4))+C`
`implies x^(-4)+y^(-4)=-4C`
`implies x^(-4)+y^(-4)=A` (where `A=-4C`)
which is the required general solution.