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Q.
The order and degree of the differential equation $ {{\left( 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right)}^{\frac{3}{4}}}={{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{\frac{1}{3}}} $ is
Given differential equation can be rewritten as $ {{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{\frac{3}{4}\times 12}}={{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{\frac{1}{3}\times 12}} $
$ \Rightarrow $ $ {{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{9}}={{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{4}} $
Here, we see that order of highest derivative is 2 and degree is 4.