A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-y=0\]
B) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2y=0\]
D) none of these
Correct Answer: B
Solution :
Key Idea: If there are \[n\] arbitrary constant, then we can differentiate maximum \[n\] times. We have, \[y=a\cos (x+b)\] ...(i) On differentiating w.r.t. \[x,\]we get \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-a\cos (x+b)\] \[=-y\] [from(i)] \[\Rightarrow \] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]
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