Question

If $ m $ and $ n $ are the order and degree of the differential equation $ {{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{5}}+4\frac{{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}}{\frac{{{d}^{3}}y}{d{{x}^{3}}}}+\frac{{{d}^{3}}y}{d{{x}^{3}}}={{x}^{2}}-1 $ , then

• A. $ m=3,\,\,n=3 $
• B. $ m=3,\,\,n=2 $
• C. $ m=3,\,\,n=5 $
• D. $ m=3,\,\,n=1 $

Answer 1

Answer: (B)

The given differential equation can be written as
$ \left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)-({{x}^{2}}-1)\frac{{{d}^{3}}y}{d{{x}^{3}}}+\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right){{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{5}}+4\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)=0 $
Clearly, its order is 3 and degree is 2. $ m=3 $ and $ n=2 $