First slide

Introduction to Differential equations

Question

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

Moderate

A

2, 2
B

2, 3
C

2, 1
D

none of these

Solution

The given equation when expressed as a polynomial in derivatives is
$ρ^{2} {(\frac{d^{2} y}{d x^{2}})}^{2} = {\{1 + {(\frac{d y}{d x})}^{2}\}}^{3}$
Clearly, it is a second order differential equation of degree 2

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