√1−x2+√1−y2=b(x−y) ⋯(1)
Clearly, the order is one as there is only one independent parameter b.
Put x=sinα,y=sinβ in eqn. (1)
⇒α=sin−1x,β=sin−1y
cosα+cosβ=b(sinα−sinβ)
⇒2cos(α+β2)cos(α−β2)=2bcos(α+β2)sin(α−β2)
⇒cot(α−β2)=b
⇒α−β=2cot−1b
⇒sin−1x−sin−1y=2cot−1b
Differentiating w.r.t. x, we get
1√1−x2−1√1−y2dydx=0
Degree of above differential equation is one.
∴α=β=1⇒α+β=2