Question

For the differential equation, find the general solution:

`x^5  dy/dx = - y^5`

Answer 1

We have, `x^5 dy/dx = -y^5`

⇒ `dy/y^5 = -dx/x^5`                         ....(1)

Integrating (1) both sides, we get

⇒ `inty^-5 dy = - int x^-5 dx`

⇒ `y^-4/-4 = - x^-4/-4 + k`

⇒ `x^-4/4 + k = (-y^-4)/4`

⇒ `(x^-4)/4 + y^-4/4 = -k`

⇒ x^-4 + y^-4 = C