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Calculus Level 3

If the curve \(y=A.e^x+B.e^{2x}+C.e^{3x}\) satisfies the differential equation \[a.\frac{d^3y}{dx^3}+b.\frac{d^2y}{dx^2}+c.\frac{dy}{dx}+d.y=0\]

Find the value of \(\dfrac{b \times c}{a \times d}\)

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