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The order and degree of the differential equation $ρ = \frac{{\{1 + {(\begin{matrix} d y \\ d x \end{matrix})}^{2}\}}^{3 / 2}}{\frac{d^{2} y}{d x^{2}}}$ are respectively

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2, 2

2, 3

2, 1

none of these

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detailed solution

Correct option is A

The given equation when expressed as a polynomial in derivatives isρ2d2ydx22=1+dydx23Clearly, it is a second order differential equation of degree 2

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The order and degree of the differential equation ρ=1+dydx23/2d2ydx2 are respectively

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The order and degree of the differential equation $ρ = \frac{{\{1 + {(\begin{matrix} d y \\ d x \end{matrix})}^{2}\}}^{3 / 2}}{\frac{d^{2} y}{d x^{2}}}$ are respectively