A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-2y=0\]
B) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=y\]
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=4y+3\]
D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]
Correct Answer: B
Solution :
Given, curve is \[y=A{{e}^{x}}+B{{e}^{-x}}\] ...(i) On differentiating w.r.t.\[x,\]we get \[\frac{dy}{dx}=A{{e}^{x}}-B{{e}^{-x}}\] Again, differentiating, we get \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=A{{e}^{x}}+B{{e}^{-x}}\] \[\Rightarrow \] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=y\] [from Eq.(i)]
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