In Problems 11-14, y = ciet + c₂e" is a two-parameter family of solutions of the second-order DE y" - y = 0. Find a solution of the second-order IVP consisting of this differ- ential equation and the given initial conditions. 11. y(0) = 1, 12. y(1) = 0, 13. y(−1) = 5, y'(−1) = −5 14. y(0) = 0, y'(0) = 0 y'(0) = 2 y'(1) = e

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Answer differential equation number 12 and 14 only

*
In Problems 11-14, y = c₁et + c₂e is a two-parameter
family of solutions of the second-order DE y" - y = 0. Find
a solution of the second-order IVP consisting of this differ-
ential equation and the given initial conditions.
= 2
11. y(0) = 1,
y'(0) =
12. y(1) = 0,
y'(1) = e
13. y(−1) = 5, y'(-1) = -5
14. y(0) = 0, y'(0) = 0
Transcribed Image Text:* In Problems 11-14, y = c₁et + c₂e is a two-parameter family of solutions of the second-order DE y" - y = 0. Find a solution of the second-order IVP consisting of this differ- ential equation and the given initial conditions. = 2 11. y(0) = 1, y'(0) = 12. y(1) = 0, y'(1) = e 13. y(−1) = 5, y'(-1) = -5 14. y(0) = 0, y'(0) = 0
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