A) 3
B) 2
C) 2/3
D) Not defined
Correct Answer: B
Solution :
[b] Degree of a differential equation is the power to which the highest derivative is raised when it is expressed as polynomial of derivatives. Given equation is \[{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2/3}}-3\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)+5\left( \frac{dy}{dx} \right)+4=0\] \[\Rightarrow {{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2/3}}=3\frac{{{d}^{2}}y}{d{{x}^{2}}}-5\frac{dy}{dx}-4\] Cube on both side. \[{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{2}}={{\left[ 3\frac{{{d}^{2}}y}{d{{x}^{2}}}-5\frac{dy}{dx}-4 \right]}^{3}}\] Hence, degree = 2
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