Find L{(t – 1) (2 – 5 sin 3t)} . O 2 5s 30s - 82+9 (s2 -9)² 2 15 15 - - s2 (s² –9) $(s2-9) 15 15 2 s2 2 - (s2+9) - g3 s2 (s² +9) 15 30s - s2+9 (s² +9)²

Q: Consider the following IVP: x" + 4x = t+4 ; x(0) = 1, x'(0) = 0 Find the general solution. A x (t)…

A: We have to find the solution of given ode using Laplace transform.

Q: Select one: 2s2 - 2s 6 S-3 O None of these 252 2s + 6 3 3s2 - 3s + 6 2 3s2 3s 6 S-2 Which of the…

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Q: dz f1-42-223)2 3 4[3-2(2+パ) a. In 3+ JE (z+1)/ J3-2(241=+C 3-4,(2+)? 3 b. 4[3-2(2+1=)] C-A(24)?…

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Q: Evaluate L{te- cos 4t} g + 2s + 15 b) (s2 + 2s + 17)2 5' + 28 - 15 b) (s + 2s + 17) s - 2s - 15 c)…

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Q: 4) USE THE GAUSS-JORDAN 2 0 -3 0 2 0 -4 1 A= 1 -1 1 - 3 0 2 1 - 4 || REDUCTION METHOD (SINE…

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Q: valuate the following: a. L {e3t + cos6t - e3t cos6t} b. L-1 {6s/(s2 + 25) + 3/(s2 + 25)} c. L-1…

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Q: z3+4z+9 Residue of f (z) at z = -1 is %3D (2z+2)(z-3)³ a. -1 64 O b. 1 64 O c. -1 32 O d. -1 16

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Q: Given: sinx = (-1)" (2п+1)! x2п+1for x € R n=0 Compute the exact value of the sum 0-1)"(2n+1) „2n+…

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Q: Let A = ° -2 [23] eAt = e2t T eAt = e³t eAt = e³t e³¹ = cos(3t) [- sin(3t) cos(2t) sin(2t) [ e37 .…

A: A square matrix A is given. The objective is to find the value of eAt. If A=a-bba, then eAt=eatcos…

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Q: Find the root of f Ca) = as +bx°+ dsinx between Xe2 and x =4 with the use of 4- Bise ction method a=…

A: Suppose the root of the function fx lies in the interval xn-1,xn. Use the following formulae, to…

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Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: Find L{(t- 1) (2 - 5 sin 3t)}. 15 30s s2+9 (s²+9)? 2 15 15 s2 (s²+9) s(s² +9) 15 15 3-号- 3? (s²–9)…

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Q: Find L[e2t+2 + e-2t cos 3t + e2t t sin(2t)] A)+ 4s-8 s+2 s-2 ((s-2)2 +4)2 (s+2)2 +9 e2 B)- s+2 s-4…

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Q: Find L {(2- t) (5 cos 3t - 1)} - 1)} 5(s² +9) 10s s2-9 (s2 –9)² 5(s²-9) 1 2 s2 10s s2+9 (s²+9)² 2. 1…

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Q: Find L[e2t t sin(2t)+ e2t+1 + e²t cos 2t] 2s-4 s+2 A)+ A) s+2 * (s-1)² +4)² (s+2)² +4 45-4 S-2 B) +…

A: Given below an detailed solution

Q: Find L{(1 – t) (3 + 2 sin 5t)} . 3 2s 10s - 82+25 (s2 –25)² - 10 20s 을 + - - s2+25 (s² +25)² 3 3 10…

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Q: Q25: A = e-2x – 3x5,B = 2Vx, C = sin³ 3x + 1 find A"" + B" - C'. (а) —8е-2х --sin 3x sin 6x – 180x?…

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Q: 4) USE THE 2 0 2 0 A 1 0 || GAUSS-JORDAN -3 0 -1 2 - 4 1 1 1 -3 -4 REDUCTION METHOD (SINE PROCEDURE)…

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Q: Find L{(t-1) (2 – 5 sin 3t)} O 2 s2 2 5s 30s - s2+9 (s² –9)² 2 2 82 15 30s s2+9 (s2 +9)² 2 _ 2 15 15…

A: We need to find the value of L{t-12-5sin3t} Formula to be used L{tkft}=(-1)kdkdsk(Lft), L{t}=1s2,…

Q: 12) The solution of 2lnx-In(x+ 2)=In2 is a) 0 b) 1 c) {-1,4) d) 4 e) поп 13) sin( 2 csc"1(2)) = b) -…

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Q: the next iterative value of the of x² - 4 = O using secant method, if the initial guess is 3 and 4

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Q: 00 n + 1 is divergent. If we multiply any constant (labeled as h)to the n + 1 such that n + 2 n=1 n…

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Q: Evaluate y" - y' - 2y = sin2x О а. у%3 (С1* e^-x) + (C2 * е^2х) - (3/20 * sin2x) + (1/20 * сos2x)…

A: Given equation is         y''-y'-2y = sin 2x Find : Complementary function The auxiliary equation is…

Q: -2s+9s2-8s+18 Find L-1 s(s²+4)(s+1) O (2- 5e +3 sin 2t) O (3 - 5e-t + 3 sin 2t) O (1-3e-t +3 sin 2t)…

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Q: when y=cos0 is horizontally factored by a factor of 1/4. y=co s1/4 θ y=cos θ + 1/4 y=1/4 cos θ…

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Q: 12. Find the general solution using Reduction of Order: a) y"= 2ln x b) y" + y' = cos 3x

A: We have to find the general solution: y''=2lnx. Here, the value of y1 is not given.

Q: Evaluate 7(t) dt: 4 4t -k; a = 0 and b = 4 t2 +1 †(t) -î + 2e4t cos t ĵ- t2 + 5t +6

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Q: 12. Find the general solution using Reduction of Order: a) y" = 31n x

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Q: 34) Ź (K²_2K) is e (n3) Ź ķ? ビ=3 Ź 2K = k=3 ntro)(2n+1), entntt) Sungs are さ。 2n3+ 3n?+n – ant- Gn…

A: We have solve the given  problem

Q: Solve the he equation F)-5y'x)+8y(x)-4y(x)-xcos(x) 41 19 41 19 sin(x)+ cos(x) -…

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Q: 2s + 5 cosh t L- s2 + 6s + 34 et 5s L-1 (s – 2)² 3t -

A: Laplace transform of the function

Q: Find L {(2 – t) (5 cos 3t – 1)}. 1 g3 10 + s2 +9 - - s2 s(s²+9) O 1 s3 10 + s2 -9 2 - - 8(s2 –9)…

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Q: Evaluate L{e* (cos at – sin nt s+3 A. (s+3)° – n² (s+3)² - – n² 2 S - 3 (s – 3)° – n² (s-3)° -R 2 2…

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Q: 7.32. Prove that for 0 sxSr, - ( (* .) cos 2r 12 (a) x(w-) cos 4x 22 cos 6z 32 6. (b) æ(r - 2) = 8 /…

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Q: Finding a Viewing WindowIn Exercises 11–30, find an appropriate graphing software viewing window for…

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Q: Theorem 8.3.3 If X ~ t(k), then E(X2r + 1) = 0 and µz, = k"- (2r – 1)(2r – 3) ... .1_ (k– 2)(k – 4).…

A: Answer: For the given theorem, The proof is:

Q: The differential operator D2- 8D+80 has the form D2- 2aD +a² + B? where a = and B= Therefore D - 8D…

A: Consider the given differential equation: D2-8D+80            f=e4xcos(8x) and g=e4x sin 8x which…

Q: Find L{(t – 1) (2 – 5 sin 3t)} . 2 2 15 15 + 83 s2 (s2 +9) 8(s2 +9) 2 15 30s s2+9 (s²+9)? 15 15 2 s3…

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Q: 5. Let a > 0, find the "generalized solution" to a" + 3x' + 2x = 8(t – a) with x(0) = 1 and æ'(0) =…

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Q: Find L[t cos 8t] s2-64 (s2+64)2 8-s (s2-64)2 64-s2 s2+64 8+s 82-64

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Q: Q25: A = e-2x – 3x5,B = 2Vx, C = sin³ 3x + find A" + B" – C'. - (а) —8e-2х sin 3x sin 6x – 180x? 1 1…

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Q: 4. Use the first Fundamental Theorem of Calculus to find 3r 2-1 dt 12 +1 sin 2z

A: Fundamental theorem of calculus Let us consider the continuous function f(x)  on the interval [a,b]…

Q: Consider the following IVP: " + 4x = t+4; x(0) = 1, x'(0) = 0 Find the general solution. (A x(t)…

A: