# `y(t)=C_1 e^{6t}+C_2 e^{-6t}` is a solution to the differential equation `y''-36y=0` where `C_1` and `C_2` are constants. Find y(t) that satisfiesy'' - 36 y = 0 y(0) = 7 y(t) = 0 as lim...

`y(t)=C_1 e^{6t}+C_2 e^{-6t}` is a solution to the differential equation `y''-36y=0`

where `C_1` and `C_2` are constants. Find y(t) that satisfies

y'' - 36 y = 0

y(0) = 7

y(t) = 0 as lim t->inf y(t)=?

y(0) = 7

y(t) = 0 as lim t->inf y(t)=?

y(t) =0 as lim t-> -inf y(t)=?

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Expert Answers

lfryerda | Certified Educator

We know that the solution to the differential equation must be of the form `y(t)=C_1e^{6t}+C_2 e^{-6t}` . Since the first condition has that `y(0)=7` , this means that `C_1+C_2=7` .

There are two other possible conditions.

**For the first infinite condition, we require the first term of the solution to vanish, which means that `C_2=7` and `C_1=0` so `y(t)=7e^{-6t}` .**

**For the second infinite condition, we require the second term of the solution to vanish, which means that `C_2=0` and `C_1=7` so `y(t)=7e^{6t}` .**