Find the Laplace Transform of the following functionss+26) f(t) =e" cos(t)Ans. F(s)=(s+2) +1A(s+ a)+ BB(s+a)² + ß²7) f(1)=e"(Acos(Bt)+ B sin(Bt) Ans. F(s)=-at8) f(t)=(1–x)u,(1)Ans. F(s)=

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Answered: s+2 6) f(1)=e" cos(t) Ans. F(s)= (s+2)°…

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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(2 cos x + 7 sin x) dx 2 ||(5sec2x- 3 csc 2x) dx 3 sect (2 tan t –6 sec t) dt 4|| (2 sin 2x – 3 cos 3x + 7) dx 5 csc u (2 csc u - 2 cot u) du sec 2x csc 2x dx 2 7|| (3 sec x + csc x) (3 sec x + csc x) dx sec2 2x dx Vtan 2x 3. Da
The derivative of f() = sin(a* + 2 a'+ 2x2 - a) is O f(#) = (4 a+6 a² + 4 * – 1) cos(a*+2 a³ +2 #² – a) O (#) = cos(4 ³ +6 a?+4* - 1) 3 O f(a) = cos(at +2 a°+2 a? – a) O f(e) = (4 a° +6 a² + 4 & – 1) cos (4 a°+ 6 a² + 4 a – 1) 3 O None of the other options.
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6) Find dy a) dx given: y = 4 +27) (use product rule) 2x2 +5 given : y=- 3x-4 b) (use quotient rule) 7) Find d [Sx)] given: f(x) = - cot x dx (simplify your answer) 1+csc(x) 8) Find [(] given: f(x)= 4. dx (3x² – 2x + 1)³
Can you write the final answer in particular solution?
a) f(x) = x-2 cos²(2x³) b) f(t) (sect + tan t)5 sec(20) c) y = 1+tan(20)
= sín(7* – by), where = az s and y = e-25, Using an appropriate chain rule, determine as O dz 7 cos(Ta – by) (-) - 6 cos(7a – 6y) (-2e) as az 7 cos(T»-6y) (-)+ 6 cos(7» - 6y) (-2e) as 7 cos(7» – by) (-) as %3D O dz :-6 cos(7» - 6y) (-2e2) as None of these.
Which of these functions (or none of them): d²z d²z satisfies the equation + ax² hay (1) z=e" (y cosx-xsin y) or (2) z=e' (ycosx-xsin.x) dy² =0?

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s+2 6) f(1)=e" cos(t) Ans. F(s)= (s+2)° +1 A(s+a)+ Bß 7) f(1)=e""(Acos(ßt)+ B sin(Bt)) Ans. F(s)= (s+a)² + ß² 8) f(t) =(t–7)u_(1) Ans. F(s)=