(a) Show that {e¬*,xe¯} is a fundamental set of solutions of y" + 2y' + y = 0 on (0, 00).

Q: It is given that 1 (x+3)(x+1) the Fundamental have / 2(x+2) (x+3)²(x+1)² * Theorem of Calculus, we 1…

A: It is given that, 1x+3x+1'=-2x+2x+32x+12. Then, by the Fundamental Theorem of Calculus, we have,…

Q: 1- iz If z = x +iy and w =- z-i show that w = 1= zis purely real

A: Use modulus property

Q: Evaluate z' if z = [1 + (x² − 1)³] ²³ O a. 2(2²-1)² (1+(2²_1)²³) i O b. none of these О с 41(2²-1)²…

A:

Q: Use the Fourier analysis to show that the Richardson's method U¡‚j+1 − Uį‚j−1 _ a² (Ui+1‚j − 2U¡‚j +…

A: As per the question, we will use the Fourier analysis to investigate the stability of Richardson's…

Q: 4. Define Let T: M2x2 (R) → P2(R) by T (a b) = (a + b) + (2d) x + ba². c d B = {69). C )·(9)· (9)}…

A: We will find the matrix with respect to the basis.

Q: f(x + h) – f(x) f'(x) = lim h-0 %3D h bsnd Diffeentinble A) 7xh2 B) 9x2h C) 5x2 D) 9x2 5) Given (x")…

A: Given that: 4. f(x+h)-f(x)=9x2h+7xh2+5h35. (xα)'=αxα-1

Q: Find the coefficient of x10 in (1 +x+x²+x³ + •..)" Find the coefficient of x' in (x +x6+x² + • ·…

A: 1)Given expression1+x+x2+x3+....nThe series 1+x+x2+x3+.... follows a geometric progression with…

Q: 7) A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is 40…

A: Given: A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is…

Q: (3) positive Verify that the fourth-order ode u - u" - u = -wu has a solution with w 3 sech( /20…

A: Given: u''''-u''-u3=-ωu  ⋯1 We have to verify this fourth-order ode. Also determine ω.

Q: Find the Wronskian of a given set {yı, y2} of solutions of 7. (1 x2)y"-2xy' (a 1)y0, _

A: Consider the given equation.

Q: prove that 01a| = 0 => a=o @ 1-al-lal @lak b ⇒-b<a<b @la-bla lal-lb/

A:

Q: (4) (LATEX question) (2018A8(b)) Use the Intermediate Value Theorem to prove that for each real…

A:

Q: hree solutions of the ODE x³y"" + 6x²y" + 4xy' - 4y = 0 are y₁ = x, y₂ = x-², and 3 = 3x-² + 8x.…

A:

Q: az + b If T(z) cz + d a, b, c, d e R. Show that T(RU{∞}) = RU {∞} if and only if exist

A:

Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Prove that if m is a positive interger, l'(-m+) = 1.3.5..(2m -1)

A:

Q: Orthonormalize [1, t, t²} in P₂(R) with (p, q) = p(0)q(0) + p(1)q(1) +p(2)q(2) }

A:

Q: Tell whether each of the following questions is biased or fair. Why? a. What type of music do you…

A: Part(a) The correct option is option A. Because in option A has the  question does not make an…

Q: Suppose f: R → R is defined by the property that f(x) = x + x² + x³ for every real number x, and g:…

A: We are given that, for all real number x,          f(x) = x + x2 + x3  And        (g o f)(x) = x…

Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (z² + 3z – 5)/2³ (3)…

A:

Q: 5. Let f(z) = 3z* + iz3 + z + 7. Prove that all roots of f (z) are in the annulus 1 < |z| < 2.

A:

Q: 4

A:

Q: - prove that = -Gtx + c 1- cosx +'x

A: To prove: ∫21-cos2x+sin2xdx=-cotx+c To prove this, take its left side and integrate after…

Q: (5) Compute -2 67 using Euler's criterion.

A: Objective: To compute -267. Concept used: Euler's criterion, is a result from number theory that…

Q: Let f(x, y, z) = x³y5 + z4 and x = (a) Calculate the primary derivatives of, of of дх' ду'dz' (Use…

A:

Q: Prove that u × 0 = 0 × u = 0.

A:

Q: 10. Subtract 2- V- 64x²y* from – 3– xy-9y' and express the result in a + bi form

A: Answer and explanation is given below

Q: 4) Find the Hermitian form [18] [2] X = H= XTAX where

A:

Q: I(¥x (P(x) v Q(x))) ^ (Vx (¬Q(x) v S(x))) ^ (Vx (R(x) → ¬S(x))) ^ (3x ¬P(x))] → 3x ¬R(x)

A: Given: To do: Prove the above statement.

Q: LET • (CX)= In [x²(x+5) ³ (x² + 4)⁰7 f'(x) = LET F(x) = \n [X²(X + 3) ³ (X² + 2)²] Cico

A:

Q: 4. a) Solve the equation 5sin-'x- 2n = 2sin-'x-3n 6) Graph, find x where f(x) = g(x), bounded by…

A:

Q: In(z,) + In(-v3 – 1) = In(2) +i %3D

A: Answer

Q: Demonstrate that x' + 3x – 8 is irreducible over Q. -

A: Given function is fx=x3+3x2−8 We have to show that fx=x3+3x2−8 is irreducible over Q(Rational…

Q: X= 2 etsin(2t) etcos(2t)

A:

Q: If the invertible function f (x) satisfies f (12) = 6, then which of the following statements is…

A: Option C is correct option.

Q: Let...

A: Given expansion formula is  a+bn=∑nkk=0nan-kbk

Q: (a) Consider the equation e'ux+2ayuy +2e*uy-sin(y) u =0, where a is a real constant. Determine the…

A: We will use basic knowledge of PDEs to answer this question.