(c) Derive the following formulae (i) Σ Fra"(n+1) 2 (ii) n(n + 1) (2n + 1) 6. r=1 (ii) 2 n(n+1 2 r-1

Q: 1) Use reduction of order method with y₁ (x) = e³x to find a second solution y2 for the DE: y" - 9y…

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Q: Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 Find the general solution. A…

A: Given Differential equation is x'' - 4x' + 4x = 4e2t

Q: 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).

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Q: by first- shifting find L(t2 e-3«) = %3D (s+3): ; * 0 a O (s+3) 2 * b O 3.cO (s+3) 3 1

A: Solution:- Correct option :- a Detailed explanation

Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

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Q: Consider y' - 2y = 3e2x with y(0) = 2. Using Runge-Kutta method with h=0.1, the k₂ needed in the…

A: Correct option is option (a) 0.80155

Q: 2. 9y" – 12y' + 4y = e-3x

A: According to our policy at Bartleby, I can solve only 1st question. Given a non-homogenous second…

Q: Q3:B. Find the convolution between the signals h[n] and x[n] shown in Figure below using analytical…

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Q: 1 Find the L-1 s(s²+2s+5) Oetsec 2t e-tcsc 2t 으글e-tsin 2t et cos 2t

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Q: 2.2 Solve y = x – y + 1 for y(0) = 1 and x = 0(0.1)0.3 , using the Runge-Kutta method of order four.…

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Q: (5 + 6t)7 16x* +6sec(x) x-3cos(x) In(x2 – 1) 2e3x + ex³

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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: TL ( - k) = | k-1 a. 6n + (n + 1)(2n + 1) - b. n(n + 1)(2n + 1) c(n²-1) C. O d. n3 e. 00 f. 플 (n +…

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Q: 5- Find L-1 5² (s²+4)² by using Convolution theorem.

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Q: Find the first term of: E (-1)n+1 (z+1)" n=1 3D1 O (z+1)^2]/2 Z+1 -(z+1) no solution

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Q: п-1 k n-2 n-1 n-2 () x6n-10 = p %3D k - 4 X6n-9 = 4 n-1 n-1 n-1 k n-1 X6n-8 = h X'6n-7 = P k n-1 n-1…

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Q: 2) Consider the equation (x – 1)y" + 3y = 0 a. Does a solution y(x) = E=0 Cnx" exist for the given…

A: given x-1y''+3y=0 claim part(a) to check whether the solution yx=∑n=0∞cnxn exist for given equation…

Q: How does h(n) = n2 / 2n behave for large whole-number values of n? Does h(n) tend to infinity?

A: Consider the function:      hn=n22n Determine end behavior for the large whole number value of n.

Q: x2n+1 El-1)"; 2n +1 n=0

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Q: 3. a. Use the Chain Rule to find N'(m) where 142.6 N(m) = %3D 1+2.38e-0.22m b. Estimate the value of…

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Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, the k4 needed in the…

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Q: Prove that L ={(1Z*)"10" | n e N}is not regular.

A: The given language: Then, the above language can be rewritten as, To prove that L is not regular.…

Q: The coefficient recursion relation for the solution Y1 = E an x"+1 of the %3D n=0 equation x2y" –…

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Q: :Find the first 3 terms for (1 (-1)*1 (2n – 1)!J n+1

A: We have to find the first three term of the given series.

Q: 15x²x³43x - 19 7. The integral (x + 1)²(x² − 6x +13) can be rewritten as C D Sax ² Ax + B +…

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Q: {in(n² +1) Im(x +4)} 19. А. В. 1 С. 1/2 D. 2 E. Divergent

A: we have to identify the given sequence is convergent or divergent

Q: Σ (-1)" Given: sin x = .2n+1 for x E R (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

A: Sum of the series, using Taylor series expansion

Q: (a) {cos ((2n + 1)E)-1 n=1 (Ъ) e2n+1 n=1 (c) n³ + n² – n2 + 3 - 1 | n=1 (d) {nsin 프}. n n=1

A: due to time limit I am able to solve first 4 part

Q: 6. Find the smallest constantr so that o(x) == x" is a solution to 3z'y" +11lry -3y= 0, for z >0 -3…

A: 6.ϕr=xr is a solution to 3x2y''+11xy'-3y=0, for x>0

Q: f(x) = xsinx (-1)"x2n (2n+2)! .2n+2 OA. (-1)"r2n+2 (2n + 1)! O B. n=1 (-1)"x2n+1 (2n+ 1)! C. 1.…

A: Maclaurain series

Q: 5) Find the general solution by using reduction of order method to t'y" – ty' – 3y = 0 given that y,…

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Q: 1. Expand x³y²(x + y)12. E15.(15) xn+3y15-n ,15-п а. n 12 b. Eo () xn+3y14–n ELo (5) xn+3y14-n С.…

A: From the given information. The given expression is .

Q: b) For n=5, calculate by applying Simpson's 1/3 and 3/8 rule together. Analytical Also get the…

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Q: x' + 2e* – In xr- 3 = 0

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Q: at k ( k) = n(k-₁) fo 1) for in

A: To prove, knk=nn-1k-1

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: n2 for all n E N. 4n Let r, :=

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Q: Describe the long run behavior of f(n) = 3n – 4n³ – 5n° + 5 As n → - 0, f(n) → ? As n → o, f(n) → ?

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Q: z/(z-3)2 dz ; C: |z+3| =3 slove by residue theorem

A: The given integral is,

Q: centered at z = -1. (-1)" (n + 1)(x + 1)" n+1 E"(z + 1)" Σ n! O m-0 El-1)~ (n + 1), (x+1)" n!

A: 1. The function given is fx=1x2. At x=-1, f-1=1. Finding the derivative of the function at x=-1. The…

Q: Formally prove the T(n) = (5n – 4)° is O(n³). Show all work and all steps to receive full credit.

A: Order: T(n)=(5n-4)3 T(n)=(5n)3-3.(5n)2.4+3.(5n).(4)2-(4)3T(n)=125n3-300n2+240n-64

Q: Q3M) Given the IVP x²y' +2xy = cosh x, y(1)=0: a) Determine the explicit solution by providing and…

A: Since we only answer one(first) of the multiple question from the given multiple no. of question.…

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: 3) Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given…

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Q: Given that n2 1 and xn =V 4n² + 3n – 2n Will {Xn}, be divergent or convergent? n=1 Will E-1 Xn be…

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Q: How does h(n) = n2 /2n behave for large whole-number values of n? Does h(n) tend to infinity?

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Q: 2. Find the general solution o- = y(1+e³) 1 له 342433434 11 11 1 "싫

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Q: S dz is 31+1 a. In(3r+1) + O a. O b. 3ln(3x +1) +C O C. None O d. -3/n(3z + 1) + C In(3z1) + C O e.…

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Q: Consider y' - 2y = 3e2x with y(0) = 2. Using Runge-Kutta method with h=0.1, the k₂ needed in the…

A: