`a) x^2 + y^2 = 1`
`==> 2x + 2yy' = 0`
`==> 2yy' = -2x`
`==> y' = (-2x)/(2y) = (-x)/y`
`==> yy' = -x`
`==> y'y' + yy'' = -1`
`==> y'^2 + yy'' = -1`
`==> yy'' = -1 -y'^2`
`==> y'' = -(1+y'^2)/y`
`==> y'' = -(1+(-x/y)^2)/y = -(1+x^2/y^2)/y = -(y^2+x^2)/y^3`
`==> y'' = -1/y - x^2/y^3`
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b)`y^2 + 2y= 2x-1`
`==> 2yy' + 2y' = 2 `
`==> y'(2y+2) = 2`
`==> y' = 2/(2y+2)= 1/(y+1)`
`==> (y+1)y' = 1`
`==> yy' + y' = 1`
`==> y'y' +yy'' + y'' = 0`
`==> yy'' + y'' = -y'^2`
`==> y''(y+1) = -y'^2`
`==> y'' = -(y'^2)/(y+1)`
`==> y'' = -(1/(y+1)^2)/(y+1) = -1/(y+1)^3`
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