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: C
Solution :
\[y=a{{e}^{mx}}+b{{e}^{-mx}}\] \[\frac{dy}{dx}=am{{e}^{mx}}-mb{{e}^{-mx}}\] \[\frac{{{d}^{2y}}}{d{{x}^{2}}}=a{{m}^{2}}{{e}^{mx}}+{{m}^{2}}b{{e}^{-mx}}\] \[\Rightarrow \] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{m}^{2}}(a{{e}^{mx}}+b{{e}^{-mx}})\] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=0\]
You need to login to perform this action.
You will be redirected in
3 sec
