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Question
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = Ax : xy′ = y (x ≠ 0)
Solution
We have, y = Ax ...(1)
Differentiating (1) w.r.t.x, we get,
y' = A ...(2)
Dividing (2) by (1), we get
`(y')/y = 1/x`
⇒ xy' = y
Hence, y = Ax is a solution of the given differential equation.
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