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1. FORMULAS TO REMEMBER L(eat f(t)) = F(s-a); c(rt-c)u₂(t)) = ecif(t)); £¹(F(s-a)) = eªt f(t) where f(t) = £¹(F(s)) ¹(e-F(s)) = f(t-c)u(t) where f(t) = ¹ (F(s)) L(f(t)8(t-c)) = f(c)e- f(t) *g(t) = [*f{r}g{t= v)dr = [*g(1)/(1-1) (F(s)G(s)) = f(t)-g(t) f(t-1)dr b) L(8(t-c)) = e-s; L(f(t) g(t)) = F(s)G(s); Find the Laplace of the following functions. a) J(t)=et et cosh(at) K(t)=sinre-+*cos(t-t)dt - İsinr

1. FORMULAS TO REMEMBER L(eat f(t)) = F(s-a); c(rt-c)u₂(t)) = ecif(t)); £¹(F(s-a)) = eªt f(t) where f(t) = £¹(F(s)) ¹(e-F(s)) = f(t-c)u(t) where f(t) = ¹ (F(s)) L(f(t)8(t-c)) = f(c)e- f(t) *g(t) = [*f{r}g{t= v)dr = [*g(1)/(1-1) (F(s)G(s)) = f(t)-g(t) f(t-1)dr b) L(8(t-c)) = e-s; L(f(t) g(t)) = F(s)G(s); Find the Laplace of the following functions. a) J(t)=et et cosh(at) K(t)=sinre-+*cos(t-t)dt - İsinr

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 do both parts and take a thumb up Plz do both parts and take a thumb up
1. FORMULAS TO REMEMBER L(eat f(t)) = F(s-a); c(f(t-c)u(t)) = e "L(f(t)); b) L-¹(F (s-a)) = eªt f(t) where f(t) = ¹(F(s)) ¹(e-F(s)) = f(t-c)u(t) where f(t) = L-¹ (F(s)) L(f(t)8(t-c)) = f(c)e-c (F(s)G(s)) = f(t).g(t) L(8(t-c)) = e-s; L(f(t) g(t)) = F(s)G(s); f(t) + g(t) = [ f(t)g{t=t}dr = [*g(1)f(t−1)dr Find the Laplace of the following functions. a) J(t)=et et cosh(at) K(t)= sin re-t+cos(t-1)dt √ sine
Transcribed Image Text:1. FORMULAS TO REMEMBER L(eat f(t)) = F(s-a); c(f(t-c)u(t)) = e "L(f(t)); b) L-¹(F (s-a)) = eªt f(t) where f(t) = ¹(F(s)) ¹(e-F(s)) = f(t-c)u(t) where f(t) = L-¹ (F(s)) L(f(t)8(t-c)) = f(c)e-c (F(s)G(s)) = f(t).g(t) L(8(t-c)) = e-s; L(f(t) g(t)) = F(s)G(s); f(t) + g(t) = [ f(t)g{t=t}dr = [*g(1)f(t−1)dr Find the Laplace of the following functions. a) J(t)=et et cosh(at) K(t)= sin re-t+cos(t-1)dt √ sine
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