Consider the homogeneous second-order Cauchy Euler differential equation

For what value α does the solution of the initial value problem comprised of this differential equation and the initial conditions y(1) = α, (1) = 6 tend to 0 as t → ∞? Enter your answer as a simplified fraction. If there is no such value of α, enter 'none'.

Question

Consider the homogeneous second-order Cauchy Euler differential equation
  
For what value α does the solution of the initial value problem comprised of this differential equation and the initial conditions y(1) = α,  (1) = 6 tend to 0 as t → ∞? Enter your answer as a simplified fraction. If there is no such value of α, enter 'none'.

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The Answer of Consider the homogeneous second-order Cauchy Euler differential equation
  
For what value α does the solution of the initial value problem comprised of this differential equation and the initial conditions y(1) = α,  (1) = 6 tend to 0 as t → ∞? Enter your answer as a simplified fraction. If there is no such value of α, enter 'none'.

Consider the Homogeneous Second-Order Cauchy Euler Differential Equation