The degree of the differntial equation ( d^ 2 y dx^ 2 )^ 2 = ( dy… - Vidyadip

MCQ

The degree of the differntial equation $\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}=\Big(\frac{\text{dy}}{\text{dx}}\Big)=\text{y}^{3}$ is:

A
$\frac{1}{2}$
✓
$2$
C
$3$
D
$4$

✓

Answer

Correct option: B.

$2$

We have,
$\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}=\Big(\frac{\text{dy}}{\text{dx}}\Big)=\text{y}^{3}$
The highest order derivative is $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}$ and its power is 2.
Hence, the degree is 2.

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