$$yy'' - 2{\left( {y'} \right)^2} + 1 = 0$$

$$yy'' + {\left( {y'} \right)^2} + 1 = 0$$

$$yy'' + {\left( {y'} \right)^2} - 1 = 0$$

$$yy'' + 2{\left( {y'} \right)^2} + 1 = 0$$