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Question
For the differential equation, find the general solution:
`x^5 dy/dx = - y^5`
Solution
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
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