A) \[3,\,\,\,2\]
B) \[2,\,\,3\]
C) \[3,\,\,1\]
D) \[3,\,\,5\]
Correct Answer: D
Solution :
Given, differential equation is \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y+{{\left( \frac{dy}{dx}+\frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{5/2}}=0\] \[\Rightarrow \] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=-{{\left( \frac{dy}{dx}+\frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{5/2}}\] On squaring both sides, we get \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}}+y \right)}^{2}}+{{\left( \frac{dy}{dx}+\frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{5}}\] Clearly, order and degree of this differential equation are 3 and 5 respectively.
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