A) \[{{m}^{2}}(a{{e}^{mx}}-b{{e}^{-mx}})\]
B) 1
C) 0
D) None of these
Correct Answer: C
Solution :
\[y=a{{e}^{mx}}+b{{e}^{-mx}};\] \[\therefore \frac{dy}{dx}=am{{e}^{mx}}-mb{{e}^{-mx}}\] Again \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=a{{m}^{2}}{{e}^{mx}}+{{m}^{2}}b{{e}^{-mx}}\] Þ \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{m}^{2}}(a{{e}^{mx}}+b{{e}^{-mx}})\Rightarrow \frac{{{d}^{2}}y}{d{{x}^{2}}}={{m}^{2}}y\] or \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\].
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