The solution of the differential equation x5(dy/dx) = -y5 will be-

The given  differential equation is

x⁵(dy/dx) = -y⁵

⇒dy/y⁵ = -(dx/x⁵)

⇒dx/x⁵ + dy/y⁵ = 0

Integrating both sides, we get:

∫(dx/x⁵ } + ∫{dy/y5} = k (where k is any constat)

⇒ (x^-4/-4)  +( y^-4/-4)  = k

⇒ x^-4 + y^-4 = -4k

⇒ x^-4 + y^-4 = C    (where C = -4k)