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A solution of the ordinary differential equation $\frac{d^{2}y}{dt^{2}}+5\frac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= -\frac{1-3e}{e^{3}}$. The value of $\frac{dy}{dt}(0)$ is _______.
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