The initial value problem y' (t) − y(t) = g(t), y(0) = 0, where (t) is the piecewise-defined function (t) = 2 if 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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The initial value problem
y' (t) − y(t) = g(t), y(0) = 0,
where (t) is the piecewise-defined function (t) =
2 if 0<t< 1
if 1≤t≤2
3
has a continuous solution on the entire interval 0<t<2. Find
that solution.
Solution:
y(t) =
if ost<1
y(t) =
if 1 ≤ t ≤ 2
Transcribed Image Text:The initial value problem y' (t) − y(t) = g(t), y(0) = 0, where (t) is the piecewise-defined function (t) = 2 if 0<t< 1 if 1≤t≤2 3 has a continuous solution on the entire interval 0<t<2. Find that solution. Solution: y(t) = if ost<1 y(t) = if 1 ≤ t ≤ 2
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