Show that the function y = ex + e–x/2 satisfies the differential equation 2y″ – y′ – y = 0.
To show: The function satisfies the differential equation .
(1) Constant multiple rule:
(2) Sum rule:
(3) Difference rule:
Obtain the first derivative of the given function .
Apply the sum rule (2) and obtain the derivative as,
Therefore, the first derivative of is .
Obtain the second derivative of .
Apply the difference rule (3) and the constant multiple rule (1) as follows
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