A) 1, 2
B) 2, 1
C) 1, 1
D) 2, 2
Correct Answer: A
Solution :
We have \[y=x\frac{dy}{dx}+\sqrt{{{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}}\] \[\Rightarrow \] \[\left( y-x\frac{dy}{dx} \right)=\sqrt{{{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}}\] \[\Rightarrow \]\[{{y}^{2}}+{{x}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}-2xy\frac{dy}{dx}={{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}\] \[\therefore \]Order and degree is 1 and 2 respectively. Note: The degree of any differential equation can be defined only when the differential equation is in the polynomial form.
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