Solve the following differential equations. Express the solution of the given initial value problem in terms of convolution integral. a) y" +w²y= g(t), y(0) = 0, y'(0) = 1 3.
Solve the following differential equations. Express the solution of the given initial value problem in terms of convolution integral. a) y" +w²y= g(t), y(0) = 0, y'(0) = 1 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.CR: Chapter 11 Review
Problem 34CR
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Plz. U need these both parts a and b neat and clean work plz i will give you thumb up
Transcribed Image Text:Solve the following differential equations. Express the solution of the given initial value problem in terms of convolution
integral.
a) y"+w²y = g(t), y(0) = 0, y (0) = 1
3.
= [te-¹f(t-1)dt, y(0) = y'(0) = 0
b) y" + 2y' + y =
Transcribed Image Text:FORMULAS TO REMEMBER
L(eat f(t)) = F(s-a); L¹(F(s-a)) = eªt f(t) where f(t) = ¹(F(s))
(f(t-c)u₂(t)) = e "Lif(t)}; L-¹(e-F(s)) = f(t-c)u(t) where f(t) = ¹ (F(s))
c(f(t) 8 (t-c)) = f(c)e-cs
(F(s) G(s)) = f(t).g(t)
f(t) + g(t) = [*f(t)g(t−r)dt = ["g(1)f(t-1)dr
L(&(t-c)) = e-s;
L(f(t) g(t))= F(s)G(s);
8
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