Let the differential equation is [1+ (d y d x )^2 ]^ 3 2 =d^2 y d… - Vidyadip

MCQ

Let the differential equation is $\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}=\frac{d^2 y}{d x^2}$. Which of the following statements is/are true?
(i) Degree of the differential equation is 2 .
(ii) Order of the differential equation is 3 .
(iii) Order and degree of differential equation respectively are 2,2 .

A
only (i)
B
only (ii)
C
only (iii)
✓
only (i) and (iii)

✓

Answer

Correct option: D.

only (i) and (iii)

(d) : The given differential equation can be written as
$
\left[1+\left(\frac{d y}{d x}\right)^2\right]^3=\left(\frac{d^2 y}{d x^2}\right)^2
$
Clearly, order and degree of given differential equation are 2,2 respectively.

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