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Question
Show the following expressions is a solution of the corresponding given differential equation.
y = aex + be–x ; y'' – y = 0
Solution
y = aex + be–x .......(1)
Differential equation: y” – y = 0
Differentiate with respect to ‘x’
y’ = aex – be–x
Again differentiate with respect to ‘x’
y” = aex + be–x
y'' = y
⇒ y” – y = 0
∴ (1) is the solution of the given differential equation.
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