The differential equation of the family of curves, \({\mathrm{x}}^{2}=4\mathrm{b}(\mathrm{y}+\mathrm{b}),\mathrm{b}\in \…

\(\mathrm{x}{\left({\mathrm{y}}^{'}\right)}^{2}=\mathrm{x}-2{\mathrm{yy}}^{'}\)

\({\mathrm{xy}}^{"}={\mathrm{y}}^{'}\)

\(\mathrm{x}{\left({\mathrm{y}}^{'}\right)}^{2}=\mathrm{x}+2{\mathrm{yy}}^{'}\)

\(\mathrm{x}{\left({\mathrm{y}}^{'}\right)}^{2}=2{\mathrm{yy}}^{'}-\mathrm{x}\)