Question

The degree of the differential equation ${\displaystyle \frac{{\text{d}}^4\text{y}}{{\text{dx}}^4}+\sqrt{1+{\left(\frac{\text{dy}}{\text{dx}}\right)}^4}}$ = 0 is

विकल्प

• 1

• 2

• 3

• 4

Answer 1

2

Explanation:

${\displaystyle \frac{{\text{d}}^4\text{y}}{{\text{dx}}^4}+\sqrt{1+{\left(\frac{\text{dy}}{\text{dx}}\right)}^4}}$ = 0

${\displaystyle \Rightarrow {\left(\frac{{\text{d}}^4\text{y}}{{\text{dx}}^4}\right)}^2={[-\sqrt{1+{\left(\frac{\text{dy}}{\text{dx}}\right)}^4}]}^2}$

${\displaystyle \Rightarrow {\left(\frac{{\text{d}}^4\text{y}}{{\text{dx}}^4}\right)}^2=1+{\left(\frac{\text{dy}}{\text{dx}}\right)}^4}$

Here, the highest order derivative is ${\displaystyle \frac{{\text{d}}^4\text{y}}{{\text{dx}}^4}}$ with power 2.

∴ degree = 2.