L[(t + 1)2e] = ? %3D s2-1 s2 +1 (s-1)2 (s – 1)2 -

Q: 2. Solve the initial value problem, D²ƒ – Dƒ = 0 f (0) = Df(0) = 1 with

A: Given  D2f-Df=0 with f(0)=Df(0)=1 The auxiliary equation is  m2-m=0 m(m-1)=0 m=0 or m-1=0 m=0, m=1…

Q: 2s + 1 7. F(s) = %3D s2 - 2s + 2 1- 2s 9. F(s) %3D s2 + 4s +5

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Q: 1– 2s F(s) = s² + 4s + 5

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Q: Solve the initial value problem. dt t-1 = 4, r(1) = 5 %3D Or-+7t + 15 6. -55 Or + 7t - 5 r= 3t + 7t…

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Q: 1 "F(s) = a. s² – 2s+17 s-1 O b. F(s) s(s? – 2s+5) 1 OC. F(s) s² – 2s+5 s-1 O d. F(s) s(s? – 2s+ 17)…

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Q: f(t) = te3t cosh 4t s²-6s+7 s2-6s-7 А. (s2-6s+25)2 С. C. (s2-6s-25)2 s2-6s+25 В. (s2-6s-7)2 s2…

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Q: 2s +10s F(s)=D (s²–2s +5)(s+1)

A: As per our guidelines we are supposed to answer only 1st one. Please repost 2nd question. Thank you…

Q: 7 (a) F(s) %3D (s+3)³ 2s – 3 ( (b) F(s) = s2 + 2s + 10

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Q: Determine L-1{F(s)} 2s+1 sF(s) + 3F(s) s2+2s+1

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Q: 4 (iv) F(s) = s2 +9 2s + 16 (v) F(s) : s2 + 4s + 20 3s – 15 (vi) F(s) %3D 2s2 – 4s + 10

A: The Laplace transform of a function is an integral that converts the real variable into complex…

Q: 3+2s 17. F(s) %3D (s+4)(s²–3)

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Q: 4. Is y = 5e-+7x e-2 a solution to the ODE y"+4y'+ 4y = 0 ?

A: The given solution is  y = 5e-x +7x.e-2x To verify it we will differentiate it

Q: -1:B: Solve the initial value problem : * d²y + 4y = 8x2 ,y(0) = -3,y'(0) = 0 dx2

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Q: determine L−1[F].

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Q: If y(s)=1/(s2-3s+2) , and y(t)=L-1(y(s)) , then y(1)=? (a) e2-e

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Q: s³-2s²+5s-9 R(s) = %3D s2(s+3)(s+1) 3s+10 W (s) %3D s(s-8)(s-6)²

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Q: S: z = √x² + y², (x-1)² + y² ≤ 1

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Q: (d) F(s) = - 1- e-s s2 +s - 2 (е) F(s) - s3 – 3s + 2

A: (-2 δ(t) + δ'(t) + δ''(t))/(s^3 - 3 s + 2) = (-2 δ(t))/(s^3 - 3 s + 2) + (δ'(t))/(s^3 - 3 s + 2) +…

Q: X(s)=(s^2+6s+7)/(s^2+3s+2) and Re{s}>-1 what is x(t)?

A: We are given : X(s)=s2+6s+7s2+3s+2 ⇒X(s)=s2+3s+2+3s+5s2+3s+2 ⇒X(s)=1+3s+5s2+3s+2 ---(1) Now,…

Q: determine L−1[F].

A: Given that, Taking inverse Laplace transform from both sides, By using L-1{aF(s)] = aL-1{F(s)}; a…

Q: [1] S(4x³ + x)V4x² + 1dx > [2] S(2x7/2 – vx)* d. [3] S V1+ 2sin3xcos3xdx

A: As per bartleby guidelines we are support to answer only 3 subparts of a question. This post…

Q: (e) Yk+1 +Yk = 1/k(k+1),

A: Given, yk+1+yk=1kk+1Substitute:yk+1=y'yk=yEquation formed is:y'+y=1kk+1A first order separable ODE…

Q: x+x-2 dx If S (x²–1)(2x-x²) dx can be resolved into A S+ Bƒ f(x)dx + D ƒ g(x)dx , then

A: Using partial fraction to solve the problem.

Q: (8 - 1)e-2s S. F(s) = s2 – 2s + 2

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Q: L(cosh 4t) = %3D .a s²-16 .b O s2 – 8 .cO s²+16 S

A: option :- a

Q: Is y=e3x−2x−3 a solution to the initial value problem shown below? y′−3y=6x+7 y(0)=−2   Yes or no?

A: Yes

Q: S₂ (1-t) ² dt 2

A: Solution

Q: 4". Sy' 8y Sx'e* y10)=8, y'l0).S X-

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Q: L(e 3t) = 1 .a O s²+3 1 b O s +3 1 S-3 .d O s2 – 3 1.

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Q: t u(t-2) L. 31 O e3-2s (s+3)² 1. 2 s+3 e-2s 1 2 (s+3)? s+3 లాఓ-5 (x+3) -6-2부 2. +. (s+3)2 +3 (6+3)2…

A: The solution is given as

Q: d³x d2x dx -2- =0 dt dr3 dr?

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Q: 3. F(s) 2(s – 1)e-25 s²+2s-2 2e-2s 4. F(s) s2–4

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Q: 3t when LI 1 ニe then L %3D S- 3 S-3

A: If Laplace transform of the function f(t) is denoted by Lf(t) or F(s), then the Laplace inverse of…

Q: y³dy 2. S. (a²-y²)7

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Q: S - 3 | c) F(s)= s2 + 4s + 3 s2 + 4s + 4 d) F(s) = (s – 1)(s – 2)(s + 4)'

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Q: 1 S² = y e2y dy

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Q: 6) y = e *(x* – 5) dy A) dx 5x² 10x + 4x3 = 21(5e* + 2x²) dy 5x2 B) = e* · 10x · 4x³ + e³* · 10x ·…

A: Let h(x) = f(g(x)) for all x, then by chain rule   h'(x)=f'(g(x))g'(x)  Also if h(x)= u(x)v(x)  Then…

Q: 3s (s-2)2 3e2 (1 – 21) 3e-21 (1 + 2t) In (출) 3te-21 3e2" (1 + 2t) 3t e2 6te2

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Q: 2e-0.8t dt, n = 5

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Q: 7. The second derivative of y = e3* + e4* is + 4e4x b. 9e3x + 16e4* а. 6e3x + 8e4x d. 9e9x + e16% C.

A: The given function is: y=e3x+e4x

Q: L() tu(t-3) e6-3s ( 1 + (s+2} 3 s+2 e2-3« ( + ) o 1 (s+2} S+2 e-3+ ( +) o 1 (s+2} s+2 ( e-6-3s 1 3 +…

A: We will find out the required value.

Q: (a) In e7 (b) eln 2 %3D (c) eln v3 %3D Preview (d) In e5

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Q: (Sx-8)3 12. g(x) = (*+3) 13. g(x) =. _(x²-s}' 14. y= 2x 15. J09=

A: Dear student,                    According to our guidelines we can answer only first question or…

Q: 4s+2 1. F(s) = s² +6s+34

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Q: What is S (x² + 2x)² dx? + x³ + ³x² + C 4 S (x² + 2x)²dx = ¹x¹ + x³ + 4 f (x² + 2x)²dx = (x² + 2x)¹…

A: We know, ∫xndx= xn+1/(n+1)

Q: determine L−1[F].

A: Given Fs=2s+3ss2-2s+5.

Q: Minimize c=s+ 2t subject to 4s +t2 270 2s +t2 190 s+ 3t 2 330 s20, t2 0. C = (s, t) =

A: The given minimize problem is C=s+2t subject to constraints, 4s+t≥2702s+t≥190s+3t≥330s≥0, t≥0   Then…

Q: D’(D² – 4)y = 3x+ 2e¬3* | y = 3x + 2e¬3x m° – 5 - 4m³ = 0 ® m' (m2 – 4) = 3x+2e-3* D (D² - 4) = 0 3…

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Q: 2s2 + s+3 F(s) = %3D (s- 1) (s+ 2)2

A: