A) \[\frac{dy}{dx}-my=0\]
B) \[\frac{dy}{dx}+my=0\]
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{m}^{2}}y=0\]
D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\]
Correct Answer: D
Solution :
\[y=a{{e}^{mx}}+b{{e}^{-mx}}\]. Differentiating, we get \[\frac{dy}{dx}=ma{{e}^{mx}}-mb{{e}^{-mx}}\]. Differentiating again, we get \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{m}^{2}}a{{e}^{mx}}+{{m}^{2}}b{{e}^{-mx}}\] \[={{m}^{2}}(a{{e}^{mx}}+b{{e}^{-mx}})={{m}^{2}}y\] or \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\].
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