Which of the following is the differential equation whose solution is \[y = a { e }^{ x } + b { e }^{ -x } \]
Answer & explanation
Correct answer: option 4
y' = \(a { e }^{ x } - b { e }^{- x } \)
\(Rightarrow y'' = a { e }^{ x } + b { e }^{- x } \)
$\Rightarrow y'' = y$
$\Rightarrow y'' - y = 0$