Order is defined as the number which represents the highest derivative in a differential equation

Second order means the order should be 2 which means the highest derivative in the equation should be or y’’

Let us examine each option given

A. (y’)² + x = y²

The highest order derivate is y’ which is first order.

B. y’y’’ + y = sinx

The highest order derivate is y’’ which is second order.

C. y’’’+(y’’)²+y=0

The highest order derivate is y’’’ which is third order.

D. y’ = y²

The highest order derivate is y’ which is first order.