What is a solution to the differential equation dy/dx=2y−1?

Joyce Sharp 2022-09-23 Answered
What is a solution to the differential equation d y d x = 2 y - 1 ?
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Answers (1)

Zackary Galloway
Answered 2022-09-24 Author has 17 answers
Substituting z = 2 y - 1 in d y d x = 2 y - 1
and considering
d z d x = 2 d y d x we have
1 2 d z d x = z . Grouping variables
d z z = 2 d x and integrating
log e z = 2 x + C 1 or equivalently
z = C 2 e 2 x = 2 y - 1 and finally
y = C 2 e 2 x + 1 2
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