The degree of the given differential equation (d²y/dx²) = √(1+ x²) is -

2

The degree of the differential equation is equal to the power of highest order derivative involve in the equation  after making the equation free from radical sign and fraction.

we have (d²y/dx²) = √(1+ x²)

squiring both sides we get 

(d²y/dx²)² = (1+ x²)

so the degree of the given differential equation (d²y/dx²) = √(1+ x²) is 2.