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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.

Advanced Engineering Mathematics
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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Plz. U need these both parts a and b neat and clean work plz i will give you thumb up
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: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 =
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
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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