In this problem, \(\displaystyle{y}={c}_{{1}}{e}^{{x}}+{c}_{{2}}{e}^{{-{x}}}\) is a two-parameter

r1fa8dy5 2022-03-22 Answered
In this problem, y=c1ex+c2ex is a two-parameter family of solutions of the second-order DE yy=0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.
y(0)=1, y(0)=8
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Answers (2)

Kingston Lowery
Answered 2022-03-23 Author has 10 answers

Solution:
y y=0 has solution y=c1ex+c2ex
where c1 and c2 are constants
so, y(0)=c1+c2=1 (i)
and; y(x)=c1exc2ex
y(0)=c1c2=8 (ii)
so, (i)+(ii) 2c1=9, c1=92
(i)-(ii)2c2=-7, c2=-72
so the solution is:
y=92ex72ex

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Jeffrey Jordon
Answered 2022-03-31 Author has 2262 answers

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