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# Consider the initial value problem d^2y/dt^23dy/dt4y=0, y(0)=a, y(0)=10 A)Find the solution of the initial value problem:

Consider the initial value problem

d^2y/dt^2−3dy/dt−4y=0, y(0)=a, y′(0)=−10

A)Find the solution of the initial value problem:

1/5e^(-t)(a(e^(5t)+4)-10(e^(5t)-1))

B) Find a so that the solution approaches zero as t→∞

a=???

I worked out question A already, but I can not figure out question B. I have tried it multiple times and just can not figure it out. Any help would be great. Thank you.