(5 — 4г If f (æ) =D which 3n n=1 following power series is / f (x) (5 — 4г)"+1 2 12n (n +1) +o0 C – n=1 (5 — 4г)"+1 4n (n+ 1) +00 C +2: -- n=1 (5 – 4æ)"+1 3п (п + 1) +o0 C+>, n=1 too (5 – 4x)"** C – 12 (п + 1) n=1

Q: Q1) Solve the following equations by the power-series method: A) xy - (x+ 2)y' +2y = 0

A: As per the guidelines I am supposed to do only one question. kindly repost the other question…

Q: 2. Express as a single power series form: > (n – 2)an+1(2x – 3)n+1+ ), an-1(2x – 3)"-1 Σ n=0 n=2

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Q: 4. Find the power series representation of the form Σ=o arn where f(x) 7 2 + x f(x) = a) Σ n=0 7·χη…

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Q: (4x+8)* What is the radius of convergence ( R) and center (a ) of the power series E 3n

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Q: Find the first three nonzero terms, or as many as exist, in the series expansion about x = 0 for a…

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Q: The equivalent series for y(x) = E=2(n – 3)a„x" %3D is : A. E=0 (n + 1)a,42x"+2 B. En=0 (n –…

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Q: 2. Express as a single power series form: 00 Σan(x - 2)² + (n + 1)an+1(x − 2)n+1 - n=2 n=1

A: Given series is           ∑n=2∞ anx-2n  +  ∑n=1∞ n+1 an+1x-2n+1    =   f n + g n…

Q: +∞ If f(x) = (x-2)¹" √n-1 O O O 1-2 n=2 V +00 Σ(-1) ¹(2-2)-1 n=2 √n-1 n(x-2) ¹√n-1 +00 -n(2-2)√√n-1…

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Q: 1 1. Write the sum of the first four nonzero terms of the power series for - (Hint: 1- 2x 1 Use the…

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Q: n! If f(x) : " and g(z) = L (- n! „x", find the power series of 1 (f(x) – g(x)). nn n=0 - n=0 n=0

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Q: Solve xy" +(1- 2x)y` +(x-1)y =0 using power series method

A: Given that xy''+(1-2x)y'+(x-1)y=0 Take y=a0+a1x+a2x2+a3x3+a4x4+a5x5+...... Take the derivative,…

Q: Which of the following is a power series representation of the function F(x) = O O O ( Σ~'((-²;-)" -…

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Q: Derive the power series solution around xo = 0 for the ODE 2x(х + 1)у" + 3 (х + 1)у' - у = 0…

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Q: Derive the power series solution around xo = 0 for the ODE 2x(x + 1)y" + 3(x + 1)y' – y = 0 %3D

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Q: Find a recurrence formula of the n" coefficient of the power series solution to the differential…

A: Given the differential equation              y''+10xy'-4y=0 Using the power series method, find a…

Q: "he reduction (recurrence) relation obtained for n 2 2 using the power series around the x = 2 point…

A: Note: n is dummy index here so we can replace n by m any time.

Q: Find distance between lines L₁:²=²=2+³ and L₂:2²-12-23 X-1 3 Z+3

A: Note:-Since you asked multiple questions,according to our policy we can answer only first question…

Q: -4 A B Given that (4r+1)(4r-3) 4r+1 4r-3' Find A and B -4 Hence, find Er=1 r=n r=D1 (4r+1)(4r-3)…

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Q: En-o(1 +)" CO 5n ii) 2n-0 100 (Зп)!

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Q: Derive the power series solution around xo = 0 for the ODE 2x(x + 1)y" + 3(x + 1)y' – y = 0 %3D

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Q: If f(x) = 3 n = 0 - and g(x) = (-1)^x, find the power series of(f(x) + g(x)) and of 1⁄(f(x) − g(x)).…

A: We are given the series       f(x) =  ∑n=0∞xnn!         g(x) =  ∑n=0∞(−1)nxnn!

Q: The first three non – zero terms in a power series expansion of the solution for IVP y' – xy' – y =…

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Q: FIND THE SOLUTION OF THE EQUATION USING THE FROBNIUS SERIES 2) 2xy" + (x+ 1)y' +3y 0

A: According to guidelines we expert can solve only one question at a time, please repost other…

Q: Q2) Find a power series solution in powers of x. Show the details (1-x²)y" - 2xy' + 2y = 0

A: Given 1-x2y''-2xy'+2y=0 Let x=1t or t=1x so that dtdx=-1x2 Now, dydx=dydtdydx=-t2dydt…

Q: 9. Find a power series representation for f(x) = = 8 4+x

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Q: Find the first three nonzero terms, or as many as exist, in the series expansion about x = 0 for a…

A: Solution:The equation isSinceThenAdd and subtract  to the left-hand side Apply the reverse product…

Q: FIND THE SOLUTION OF THE EQUATION USING THE FROBNIUS SERIES 1) ry" + 4xy' +2y 0 2) 2xy" + (x + 1)y'…

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Q: Find the first three nonzero terms, or as many as exist, in the series expansion about x = 0 for a…

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Q: The value of n such that ph pn-1 || 553,5 ,n> 4 is 15.

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Q: Which of the following power series must be used as the nonhomogeneous part for the given initial…

A: According to the boundary condition y(1/2) = 1. Thus the option satisfying the boundary condition…