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