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) None of these
Correct Answer: C
Solution :
Given equation is \[y=a{{e}^{mx}}+b{{e}^{-mx}}\] On differentiating w.r.t. x, we get \[\frac{dy}{dx}=m\,a{{e}^{mx}}-m\,b{{e}^{-mx}}\] Again differentiating, we get \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{m}^{2}}\,a{{e}^{mx}}+{{m}^{2}}b{{e}^{-mx}}\] \[={{m}^{2}}(a{{e}^{mx}}+b{{e}^{-mx}})={{m}^{2}}y\] \[\Rightarrow \] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\]
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