Answer :

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 = y^{2}

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’ = y^{2}

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

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