1.

Verify that the given function (explicit or implicit) isa solution of the correseponding differential equation : y = sqrt(1 + x^2): y' = (xy)/(1 + x^2)

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SOLUTION :`y = sqrt(1 + x^2)`
`y.= 1/(2 sqrt(1+x^2)) (0+2x)`
`=x/sqrt(1+x^2) = (xsqrt(1+x^2))/(1+x^2) = (xy)/(1 + x^2) `
`THEREFORE y = sqrt(1 + x^2)` is a solution of `y. = (xy)/(1+x^2)`


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