Consider the integro-differential equation dy + 4| dt [ relt-r)dr y(T)dr + 4y(t) = subject to | y(T)dt = 1 and y(0) = 0. (a) Find Y(s), the Laplace transform of y(t). (b) Use your result from part (a) to express y(t) in the form y(t) = A+ Bf1(t) + C f2(t) + Df3(t). Note: you do not need to find the real constants A, B,C, D.
Consider the integro-differential equation dy + 4| dt [ relt-r)dr y(T)dr + 4y(t) = subject to | y(T)dt = 1 and y(0) = 0. (a) Find Y(s), the Laplace transform of y(t). (b) Use your result from part (a) to express y(t) in the form y(t) = A+ Bf1(t) + C f2(t) + Df3(t). Note: you do not need to find the real constants A, B,C, D.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
Related questions
Question
Transcribed Image Text:Consider the integro-differential equation
dy
+ 4
dt
y(T)dt + 4y(t) =
relt-r)dt
subject to
y(T)dt = 1
and
y(0) = 0.
(a) Find Y(s), the Laplace transform of y(t).
(b) Use your result from part (a) to express y(t) in the form
y(t) = A+ Bf1(t) + C f2(t) + Df3(t).
Note: you do not need to find the real constants A, B,C, D.
Expert Solution
Step 1
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning