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Verify that the given functions (explic...

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:`y=sqrt(1+x^2)` : `yprime=(x y)/(1+x^2)`

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`=> y′=(xy)/(1+x^2)​`
`⇒(dy)/(dx)​=(xy)/(1+x^2)`​
`⇒(dy)/y​=(xdx)/(1+x^2)`
`⇒∫(dy)/y​=∫(xdx)/(1+x^2)`
​ Let `x^2+1=t`
`=>2xdx=dt`
`=>xdx=(dt)/2`​
So,from equation,
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