question_answer

Which of the following differential equations has the same order and degree  [Kurukshetra CEE 1998]

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

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

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

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