OrnaVerum
v 6.30.00
28 Jan 2022
updated 28 Jan 2022

Eqn 12c Help

Given that
y
a
dy
 = 
x
0
½ (ex/a – e–x/a) dx

we can represent this in terms of the antiderivatives (indefinite integrals) and their specified limits as

y
y
|
a
 =  (a/2) (ex/a + e–x/a)
x
|
0

which becomes

(y – a) = (a/2) {(ex/a + e–x/a) – (e0 + e0)}
(y – a) = (a/2) {(ex/a + e–x/a) – 2}

and finally

y = ½ a (ex/a + e–x/a)