Consider the initial value problem (0 y+3y=10 0 if 0 < t <3 if 3
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.6: Applications Of Differential Equations
Problem 15E: Solve Exercise 14 if a 25 solution of the same mixture is added instead of pure alcohol.
Question
15
Transcribed Image Text:Consider the initial value problem
(0
y+3y=10
0
if 0 < t <3
if 3 <t<6
if 6 <t<00,
y(0) = 3.
a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation.
Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get
to part (b) below).
SY(s)-3+3Y(s) help (formulas)
b. Solve your equation for Y(s).
Y(s) = £{y(t)} =
c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).
y(t)
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