Q11Multiple choice
Find the degree of the differential equation ${{\left( \frac{{{\text{d}}^{\text{2}}}\text{y}}{\text{d}{{\text{x}}^{\text{2}}}} \right)}^{\text{3}}}\text{+}{{\left( \frac{\text{dy}}{\text{dx}} \right)}^{\text{2}}}\text{+sin}\left( \frac{\text{dy}}{\text{dx}} \right)\text{+1=0}$.
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Ans: The given differential equation is ${{\left( \frac{{{\text{d}}^{\text{2}}}\text{y}}{\text{d}{{\text{x}}^{\text{2}}}} \right)}^{\text{3}}}\text{+}{{\left( \frac{\text{dy}}{\text{dx}} \right)}^{\text{2}}}\text{+sin}\left( \frac{\text{dy}}{\text{dx}} \right)\text{+1=0}$.
The differential equation is not polynomial in its derivative because of the term $\text{sin}\left( \frac{\text{dy}}{\text{dx}} \right)$ thus its order is not defined.
The correct answer is (D).