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Q. Find the order and degree of the differential equation $y=x\left(\frac{dy}{dx}\right)+\sqrt{{a}^{2}{\left(\frac{dy}{dx}\right)}^{2}+{b}^{2}}$

(vi) Ans : Degree - 2, Order - 1

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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