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Q. Find the order and degree of the differential equation y = x d y d x + a 2 d y d x 2 + b 2
(vi) Ans : Degree - 2, Order - 1
 

Hello Shubhrajyoti,
given y = x (dy/dx) + ​√{a^2(dy/dx)^2 + b^2}
=> y - x(dy/dx) = ​√{a^2(dy/dx)^2 + b^2}
Squaring 
[y - x (dy/dx)]^2 = {a^2(dy/
dx)^2 + b^2}
After squaring and rearranging some how we have (dy/dx)^2
Hence degree is 2 and order is 1
If we have d^2y/ dx^2 then we would say order as 2 but we have only dy/dx
And highest power is only 2. Hence degree is 2

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