Consider the initial value problem y' + 4y = 16t, y(0) = 6. 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). b. Solve your equation for Y(s). Y(s) = L{y(t)} = = ‒‒‒ www www = help (formulas) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = #
Consider the initial value problem y' + 4y = 16t, y(0) = 6. 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). b. Solve your equation for Y(s). Y(s) = L{y(t)} = = ‒‒‒ www www = help (formulas) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = #
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the initial value problem
y' + 4y = 16t,
y(0) = 6.
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).
b. Solve your equation for Y(s).
Y(s) = L{y(t)} =
=
‒‒‒
www
www
=
help (formulas)
c. Take the inverse Laplace transform of both sides of the previous equation to
solve for y(t).
y(t) =
#
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Step 1: Find the laplace transform of the given initial value problem
VIEWStep 2: Take the laplace transform of equation (1) both side
VIEWStep 3: Find the value of A, B and C using partial fraction method
VIEWStep 4: Simplify the expression for A and B
VIEWStep 5: Take the inverse laplace transform of equation (4)
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