Consider the initial value problem
y
′
′
−
3
y
′
−
10
y
=
0
,
y
(
0
)
=
α
,
y
′
(
0
)
=
4
\displaystyle {y}{''}-{3}{y}'-{10}{y}={0},\quad{y}{\left({0}\right)}=\alpha,\quad{y}'{\left({0}\right)}={4}
y
′′
−
3
y
′
−
10
y
=
0
,
y
(
0
)
=
α
,
y
′
(
0
)
=
4
Find the value of
α
\displaystyle \alpha
α
so that the solution to the initial value problem approaches zero as
t
→
∞
\displaystyle {t}\to\infty
t
→
∞
α
\displaystyle \alpha
α
=
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\displaystyle
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity