A) \[2,2\]
B) \[1,1\]
C) \[1,2\]
D) \[2,1\]
Correct Answer: A
Solution :
Given differential equation is \[y=\left( \frac{dp}{dx} \right)x+\sqrt{{{a}^{2}}{{p}^{2}}+{{b}^{2}}},\left( p=\frac{dy}{dx} \right)\] \[\Rightarrow \]\[y=\left[ \frac{d}{dx}\left( \frac{dy}{dx} \right) \right].x+\sqrt{{{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}}\] \[\Rightarrow \]\[\left( y-x\frac{{{d}^{2}}y}{d{{x}^{2}}} \right)=\sqrt{{{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}}\] \[\Rightarrow \]\[{{\left( y-x\frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}={{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}\] Hence, order\[=2\]and degree\[=2\]
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