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If y=A e^(m x)+B e^(n x), show that (d^2...

If `y=A e^(m x)+B e^(n x)`, show that `(d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y=0`

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To show that \( \frac{d^2y}{dx^2} - (m+n)\frac{dy}{dx} + mn y = 0 \) for the function \( y = A e^{mx} + B e^{nx} \), we will follow these steps: ### Step 1: Differentiate \( y \) with respect to \( x \) Given: \[ y = A e^{mx} + B e^{nx} \] ...
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