" when y(0) = -1 t > // Problem 3. Solve the following IVP using a Laplace transform. (2 cos(t), t.
" when y(0) = -1 t > // Problem 3. Solve the following IVP using a Laplace transform. (2 cos(t), t.
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.
Chapter4: Calculating The Derivative
Section4.5: Derivatives Of Logarithmic Functions
Problem 47E
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Transcribed Image Text:"
when y(0) = -1
t > //
Problem 3. Solve the following IVP using a Laplace transform.
(2 cos(t), t</
y'(t) − y(t)
=
0
ล
Make sure to follow the following outline, and box these intermediate points along the way:
⚫ Rewriting the function g(t)
(2 cos(t), t</
in terms of the unit step function.
⚫ Finding the appropriate transformation of the ODE using the Laplace transform.
● Solving the resulting equation for Y(s) = &{y(t)}
Taking the inverse Laplace transformation to find y(t).
• Writing your final answer as a piecewise function (that is, without the unit step
function).
• Graphing your solution (using Desmos).
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