question_answer

Which of the following differential equations has the same order and degree?

A)  \[\frac{{{d}^{4}}y}{d{{x}^{4}}}+8\,\,{{\left( \frac{dy}{dx} \right)}^{6}}+5y={{e}^{x}}\]

B)  \[5\,\,{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{4}}+8\,\,{{\left( 1+\frac{dy}{dx} \right)}^{2}}+5y={{x}^{8}}\]

C)  \[{{\left[ {{\left( 1+\frac{dy}{dx} \right)}^{3}} \right]}^{2/3}}=4\,\,\frac{{{d}^{3}}y}{d{{x}^{3}}}\]

D)  \[y={{x}^{2}}\frac{dy}{dx}+\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{2}}}\]

E)  None of these