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  • y=ae^{mx}+be^{-mx} satisfies which of the following differential equation. a.frac{dy}{dx}+my=0 b.frac{dy}{dx}-my=0 c. frac{d^{2}y}{dx^{2}}-m^{2}y=0

y=ae^{mx}+be^{-mx}  satisfies which of the following differential equation.

\\a.\;\; \frac{dy}{dx}+my=0\\\\ b.\;\; \frac{dy}{dx}-my=0\\\\ c.\;\; \frac{d^{2}y}{dx^{2}}-m^{2}y=0\\\\ d.\;\; \frac{d^{2}y}{dx^{2}}+m^{2}y=0\\

Answers (1)

given y=ae^{mx}+be^{-mx}

upon differentiation, we get \frac{dy}{dx}=a.me^{mx}-b.me^{-mx}

after differentiation again we get

\frac{d^{2}y}{dx^{2}}=am^{2}e^{mx}-bm^{2}e^{-mx}\\\\ \Rightarrow \frac{d^{2}y}{dx^{2}}=m^{2}\left (ae^{mx}-be^{-mx} \right )\\\\ \Rightarrow \frac{d^{2}y}{dx^{2}}=m^{2}y\\\\ \Rightarrow \frac{d^{2}y}{dx^{2}}-m^{2}y=0\\

Option c is correct

Posted by

infoexpert24

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