question_answer

Find the value of m and n, where m and n are order and degree of differential equation \[\frac{4{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}}{\frac{{{d}^{3}}y}{d{{x}^{3}}}}+\frac{{{d}^{3}}y}{d{{x}^{3}}}={{x}^{2}}-1.\]

Answer:

Given, \[\frac{4{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}}{\frac{{{d}^{3}}y}{d{{x}^{3}}}}+\frac{{{d}^{3}}y}{d{{x}^{3}}}={{x}^{2}}-1\] \[\Rightarrow \]   \[4{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}+{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2}}=({{x}^{2}}-1)\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)\] \[\therefore \]Order of differential equation (m) = 3 and degree of differential equation (n) = 2