4 The value of 2 n=1 3n2 will be + 6n .... .

Q: 5. Solve the initial-value problem x' = Ax, x(0) = x, where, 2 -5] 2 ,x(0) = 3 %3D 4 -2

A: Explanation of the solution is given below...

Q: Consider the following initial-value problem, 1 1 a' (t) + u(2) : 3. u(t) = t t - 1 with What is the…

A: The solution is given as follows

Q: Solve the following initial value problem and present its particular solution: ?"+?′+9.25?=0,…

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Q: 23 4- [fe** dycdx ans :(e' - e' )(e² – e') 12

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Q: Solve the initial value problem. d²s_ dt² 34) -128cos (8t), s (0) = 6, s(0) = 8

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Q: Eo[(n + 2)(n + 1)an12 + (3n – 1)an]æ" = 0 - The initial conditions are y(0)=2 and y'(0)=0.

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Q: 2. у" — бу' + 7у %3D0

A:

Q: 3) Find the particular solution of the DE y" = 12x² if y(0) = 1 and y'(0) = 2.

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: Solve the initial-value problem (-1, 00): on (2x + 3)y" – (2x + 5)y' + 2y = (2x + 3)?e2 y(0) = 0,…

A:

Q: Consider the initial value problem 0 ÿ' = = [2²2 ÿ+ģ(t), 4t 2t² -1 Suppose we know that 0 = - [2] -2…

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Q: (-2)"+1 n+ 5" (2n)! 2n - n! - n (a) (b) (-1)". n=1 n=1 (c) E(-1)": (n!)'3" (2n + 1)! (d) 5 (-1)"…

A:

Q: 7. Find k > 0 and m E N so that 6n3 + 17n m.

A: The solution of given problem as follows :

Q: Solve the initial value problem by finding the particular solution бу + у 3 6 сosh x, у(0) — 0.2,…

A: The given differential equation is  8y''-6y'+y=6 cosh x  , y(0)=0.2, y'(0)=0.05 Firstly finding the…

Q: Solve the initial value problem. ds 12t(31 - 1)°, s(1) =7 dt The solution is s = S.

A:

Q: Solve the initial-value problem x' = Bx, x(0) = xI for the following B and xI.

A: Part A)- Given: Given matrix B=-2-11-4,x'=30 We want to find solution of x'=Bx Solution: We want to…

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

A:

Q: Solve the initial value problem ty"+ty'–y=2, y(0)=-2, y'(0)=-3. Evaluate y(1)?

A: We will solve the problem using laplace transform. We know formula L[f(t)]s=∫0∞f(t)e-stdt…

Q: Choose one = If yo 15, then the solution of the initial value problem (c) is the largest one for…

A:

Q: 3) Solve the initial value problem : 1 ?Y(1) = 5. yY = 3x? 2

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Q: 1 Find the general Solution of the following equa tion ; xy'-2y=x²

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Question 3. Show that n3 + 4n2 +1 O(n²). %3D n+3

A: See the attachment

Q: Solve the initial value problem. ds 281(7? – 5)°, dt s(1) = 12 4 (71² – 5) + 4 The solution is s = 2

A: This is a problem of integration. By using below formula we will calculate integral and then will…

Q: A radioactive sample decays according to the law - -hy where k>0 Suppose c represents the size of…

A: From the given differential equation:   dydt=-ky   So, dy=-kydt...Integrating on both…

Q: 11. One of the following could be a series solution for y + 5xy + y = 6 lnx + 4 where y (1) = –1, y…

A: Taylor series of a function f(x) about x=a is given by:…

Q: 16. Find all solutions in the range (0 <0 < 2n): 20sin20 – 5 = 0

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Q: Solve the initial-value problem. 2xy' + у %3D бх, х> 0, у(4) %3D 20

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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: 1 Given: E = 3 -1 [-2 2 01 2, find E1. 3 -2] 2 -1 11 a. -2/3 -5/3 2 c. nonsingula -1] 4/3 -5/3 b.…

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Q: Find the radius of convergence and interval of convergence of  Σ 1 to infinity…

A: Given

Q: (b) Ln=3 n-ln n-(In(ln n))P (a) En=1 ' pn=qn• (0 < q < p)

A: In this question, we find the value of p for the series is convergent.

Q: 9. Solve the following equation. sec x - 2 -0 A) 元 x -+ 2n and x- 2n7, where n is an integer 6 B) x…

A: Given: sec x-2=0

Q: In 5 e'dt 2t e 0 V e 2t + 64

A:

Q: 8. The solution of the initial-value problem x' = 5 )x, x(0) = х, is: (o) x =*" ()-*() 6) x = +()+**…

A:

Q: Solve the following initial value problem. dr = - Tcos n0, r(2) = 3 r= de

A: Given, drdθ=-πcosπθr2=3

Q: Solve the given initial-value problem. I'= 2r, -1- 4x, + 2et x= 2x, - 4x, + 3et 1, =x-21, +et given…

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Q: Question 4 4.1.a q(t) = t°In(t³) q(1) = 2t In(e*) + *(: 2 5t 5 2t In In (t) + 5t

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Q: III. Solve the initial – value problem: + xdy=0 ;y(1) =n

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Q: solve for the value of i + = In 1 In e -1

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Q: у" — бу' + 13у %3D 0, у(3 - 6y'(9) =7 ||

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Q: e initial-value problem () - († )(). ) - () d 1 |

A:

Q: solution

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Q: A-() Solve the initial value problem = A with 7(0) =

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Q: Solve the following initial-value problem.   ?′′+16?=0,     ?(0)=2,    ?′(0)=−8

A:

Q: The form of the exact solution to 2 + 3y = e, where y(0)=5, is O 5e -1.5z + xe- O 5el.5 + e- O None…

A:

Q: The population of two different species are given by P1 P1 = 4e0.6t - and P2. where t is measured in…

A: The population of two different species are given by, P1=4e0.6tP2=9e0.4t

Q: (b) Solve the initial value problem z(0) - () |ã, #(0) =

A: firstly we find eigenvalues and then find corresponding eigen vectors and after that find general…

Q: 7. E(-1)"- Vn +1 n=1

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Q: n +1 5n An bn n + 2' 4n2 – 3' { 400/n -1/(400n2) n even { Į 7 n/(1+n²) 1 901 п оdd Cn dn

A:

Q: by first – shifting find L(e2tt3)= - 6. (s-2)4 .a O | 1 (s-3)4 bO (s – 3) 4 6. (s -2)3 cO 3 (s–2) 4…

A: Laplace transform

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

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.