Question

Find the order and degree of the differential equation $ {{\left( \frac{{{d}^{4}}y}{d{{x}^{4}}} \right)}^{3/5}}-5\frac{{{d}^{3}}y}{d{{x}^{3}}}+6\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+5=0 $

• A. $ 4,\,\,3 $
• B. $ 3,\,\,4 $
• C. $ 4,\,\,5 $
• D. $ 5,\,\,4 $

Answer 1

Answer: (A)

$ {{\left( \frac{{{d}^{4}}y}{d{{x}^{4}}} \right)}^{3/5}}-5\frac{{{d}^{3}}y}{d{{x}^{3}}}+6\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+5=0 $
$ \Rightarrow $ $ {{\left( \frac{{{d}^{4}}y}{d{{x}^{4}}} \right)}^{3}}={{\left( 5\frac{{{d}^{3}}y}{d{{x}^{3}}}-6\frac{{{d}^{2}}y}{d{{x}^{2}}}+8\frac{dy}{dx}-5 \right)}^{5}} $
Which is the differential equation of order $ 4 $ and degree $ 3 $ . (because order is equal to highest order derivative and degree is equal to highest power of highest order derivative).