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Consider the initial value problem 2y′′+11y′+5y=aδ(t−1), y(0)=y′(0)=0 , where δ denotes the impulse function. Suppose that...

Consider the initial value problem 2y′′+11y′+5y=aδ(t−1), y(0)=y′(0)=0 , where δ denotes the impulse function. Suppose that the solution of this initial value problem satisfies y(3)=(e^9−1)/e^10. Find the value of a.

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