5. Solve the following initial value problem (IVP)-xy = x v(0) = Ey(0) = 1by using(a) second-order Taylor's series method with h = 0.2 and 0

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Answered: 5. Solve the following initial value…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Find the series solution (x > 0) for the following equations. (a) zy' +ry + (2? 6. y = 0; (b) 2y'+ ry + (r- 2)y = 0.
4
Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.) (x – 1)y" – xy' + y = 0, y(0) = -4, y'(0) = 5 y =
Q3/ Compute the first three terms of the Taylor series method to obtain a solution of y=-xy correct to four decimal places for values xo = 0.0, x₁ = 0.1, x2 = 0.2 dx and .x3= 0.3 with the initial condition y(0) = 1 and let h = 0.1?
Q 3. Find the Taylor series of f at the point c for : (c) f(x) = sin x, c= T (d) f(x) = cos x, c = 5 (a) f(x) = e", c= 2 (b) f(x) = }, c = 1
1. The function f(x) satisfies: f(0) = 0; f'(0) = -1; f" (0) = 4; f"" (0) = 54, and f(4) (0) = 8. Find the first four non-zero terms of the Maclaurin series for this function. OA. -x+4x2+54x³+8x4 OB. None of these OC.-x+ 2x² + 9x³ + x4 OD. -1+ 4x + 27x² + x³ OE.-x+ 2x²+18x³ + 2x4
Determine the 6th order power series solution of the following ODEs with initial values. a. f''(x)-3f'(x) +2f(x) = 4 with f(0)= 1 and f'(0) = 0 Note: f''(x) = 4 + 3f'(x) - 2f(x) such that f'''(x) = 3f"(x) - 2f'(x) b. f"(x) + f(x) = x with f(0) = 0 , f'(0) = 2 Note: f''(x) = x - f(x) such that f'''(x) = 1-f'(x) and f4(x) = -f''(x)
3. Find the Taylor series of f (x) = 32x at a = 1 (five terms). %3D 1-cos2x 4. Find lim using series. x→0 1+3x-e 3x 5. Find the power series of f (x) = - using binomial series (five terms).
Can you help me with part b. I thought guidlines says 2 problems anyways i put the first one there just for reference. Thanks...
Use power series to solve the initial-value problem (x² – 2)/" + 10xy + 8y = 0 , y(0) = 1, y (0) = 0 . Answer: y = > 1 a2n +> x2n+1. n=0 n=0
1. Use zero-through third-order Taylor series expansions to predict (3) for fix)=25x³-6x² + 7x+88 using a base point at x = 1. Compute the true percent relative error &, for each approximation. h = 3-1=2 Record your result on the table. 2.. Use zero-through third-order Taylor series expansions to estimate f(x) = e-* using a base point at x = 1 for x = 0.2. Compute the true percent relative error E, for each approximation. A = 0.8 Record your result on the table. Order 0 1 2 3 Order 0 1 2 3 Value Value E₁ E₁
Find the following coefficients: CO (3).³ C1 = C3 = C₂ = Represent the function f(x) - -.7 .3(3)¯ —.21(3) 2! .357(3) 3! -1.7 -2.7 = x0.3 as a power series: Σen (x − 3) n n=0

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5. Solve the following initial value problem (IVP) - xy = x y(0) = E by using (a) second-order Taylor's series method with h = 0.2 and 0sxS1. (b) second-order Taylor's series method with h = 0.1,0.25,0.5 and 0