A) \[{{{y}'}'}'-{y}'=0\]
B) \[{{{y}'}'}'-{{y}'}'+{y}'=0\]
C) \[{{{y}'}'}'+{{y}'}'=0\]
D) \[{{y}'}'+{{y}'}'-{y}'=0\]
Correct Answer: C
Solution :
Given \[y=A+Bx+C{{e}^{-x}}\] ?..(i) Þ \[\frac{dy}{dx}=B-C{{e}^{-x}}\] .?.(ii) Þ \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=C{{e}^{-x}}\] .?.(iii) and \[\frac{{{d}^{3}}y}{d{{x}^{3}}}=-C{{e}^{-x}}\] ?.(iv) Adding (iii) and (iv) we get, \[\frac{{{d}^{3}}y}{d{{x}^{3}}}+\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\] i.e., \[{y}'''+{y}''=0\].
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