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Consider the initial value problem $dt_{2}d_{2}y −3dtdy −4y=0,y(0)=a,y_{′}(0)=−5$ (a) Find the solution of the initial value problem: $y(t)=−(5−5+a +a)e_{−t}+(5−5+a )e_{4t}$ (b) Find $a$ so that the solution approaches zero as $t→∞$. $a=$

The given differential equation is

Let be a trial solution of

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