y = a{e^{mx}} + b{e^{ - mx}} satisfies which | vedclass

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(D) Given the equation: $y = a{e^{mx}} + b{e^{-mx}}$Differentiating with respect to $x$,we get:$\frac{dy}{dx} = ma{e^{mx}} - mb{e^{-mx}}$Differentiati

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$\frac{d^2y}{dx^2} - m^2y = 0$

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(D) Given the equation: $y = a{e^{mx}} + b{e^{-mx}}$Differentiating with respect to $x$,we get:$\frac{dy}{dx} = ma{e^{mx}} - mb{e^{-mx}}$Differentiating again with respect to $x$,we get:$\frac{d^2y}{dx^2} = m^2a{e^{mx}} + m^2b{e^{-mx}}$Factoring out $m^2$:$\frac{d^2y}{dx^2} = m^2(a{e^{mx}} + b{e^{-mx}})$Since $y = a{e^{mx}} + b{e^{-mx}}$,we can substitute $y$ into the equation:$\frac{d^2y}{dx^2} = m^2y$Rearranging the terms gives:$\frac{d^2y}{dx^2} - m^2y = 0$Thus,the correct option is $D$.

$y = a{e^{mx}} + b{e^{ - mx}}$ satisfies which of the following differential equations?

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