2. Find the series solution of the equation xy" + 2y' + xy = 0 in a form: y(x) = y(x)=(ao )=²(ao c cos x + a₁ sin x), where, X x5 x7 x cos x=1- + +... and sin.x = x- - 2! 4! 5! 7! 6! ... 3! +... ***

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Q: (a) (i) Q8 (b) char(Z₂ × Z7X Z₁4) = 14 (c) Z₂ × Z7 × Z12 = Z14 × Z12

A: a) TRUE b) TRUE c) TRUE

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Q: 20. As shown in the required readings or videos 1. Prove that the gamma function r(x) = ftx-¹e-dt…

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Q: Q4. Solve the given ODE using the method of undetermined coefficients. - y" - 4y = (x² − 3)(sin2x)

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Q: Example 8.28. Apply Simpson's rule to evaluate the integral p26_p4# dxdy 1=5₂8 5²4 I xy

A: To evaluate the integral I=∫22.6∫44.4dxdyxy using Simpson's rule.

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Q: A O 5 B 15 D 11 19 16 18 10 Given the Venn diagram as shown above, answer each of the following…

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Q: 3. Find the maximum and minimum values of z-a 1 āz on |z| ≤ 1 (where a with la| < 1 is fixed)

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Q: solve by finite difference ²x - ²)x=t dt²

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Q: 5: Let R=(Z,+, .). Find Chan Idempotent element of R e) Is R a field? Why? c) Nilpotent elements of…

A: We have to find the nilpotent and idempotentent element of R.

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Q: 8) Find the Laurent series of f(z) = (z-1)(z-2) b) ·+3+3+3+3+3² +22² +22³ **** + c) .... + I d) NOTA…

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Q: Example 9.14. Solve yx+1Y+ (x + 2)yx+1 + xy + x² + 2x + 2 = 0

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Q: Exercise 8.1.15. Suppose N G. If N is abelian, and G/N is abelian, does G have to be abelian? Give a…

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Q: -2 (x) 1/2 [ 2 X

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Q: A subset (a,b) ≤R is T2-space in (R,Tu) * 1 true 2 False

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Q: 1) For ellipse, consider the following graphs 0 O Please use your own words to summarize the…

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Q: 4. Read this problem carefully. Row reduce the matrix to reduced echelon form. Circle the pivot…

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Q: Example 8.27. Using trapezoidal, rule, evaluate I = ²² dxdy, taking four sub-intervals. 11 J1 x + y

A: problem is solved using trapezoidal rule.

Q: The approximation to a root of the equation x^2+x-1=0 in the interval [0,1] b applying the regula…

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Q: 1. Compute u + v and u-2v where u = -5 and v = T 2

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Q: Use z scores to compare the given values. The tallest living man at one time had a height of 246 cm.…

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Q: 1. The Laplace transform of the function y(t) = t5 is a. 20/s5 b. 1/(s-5)6 c. 120/s6 2. The Laplace…

A: Note: Hi! Thank you for the question, As per the honour code, we are allowed to answer three…

Q: Consider the ring homomorphism : I→ R defined as (a) Show that is a ring homomorphism. (b) Use FIT…

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Q: xample 8.19. Use Romberg's method to compute ax correct to 4 decimal places. 2 0 1 + x²

A: Solution :-

Q: 3. Find the maximum and minimum values of z-a 1-āz on 2 ≤ 1 (where a with a < 1 is fixed)

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Q: If f(z) = u-iv is analytic in the z-plane, then the C-R equations satisfied by it's real and…

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