y" - 22y' + 121y = 1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function n(x) = C₁ y ₁ (x) + C₂ Y₂ (x) = C₁ +C₂ e-11x 1+x2¹ y(0) = -10, y'(0) = 6. IOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) # C₁9(x) + C₂f(x). e-11x 1+x2 is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x) = = 2) The particular solution y(x) to the differential equation y" + 22y' + 121y = and u₂(x) = + 3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y = e-11x 1+x2 dt + is dt

Q: Let p ∈ R, and ε > 0. Using The Density theorem, show that B(p, ε) ∩ Q contains at least two…

A: Introduction: The density property is a very significant property of the field of real numbers.…

Q: Verify that the set C[a, b] of all continuous real-valued functions defined on the interval a ≤ x ≤…

A:

Q: Solve y (kx √√3) dx + (√3 − kx) dy O a. 2kx + 4√/31n|kx √3- O b. 2kx + 4√3ln|kx c. 2kx + 4√3 ln | kx…

A:

Q: Karin has 2,000dollars in notes. The banknotes are in denominations of 20dollar and 100dollar. Karin…

A:

Q: Theorem Let fbe a continuous function on an open subset U of a anach space X into a Banach space Y.…

A:

Q: Find g(t) solution of the initial value problem '-4y/+13y=38(t-5), g(0) = 1, g(0) = 0, where 8(t) is…

A:

Q: -[ 8 3 -15 5 2 Find enough vectors to form a basis of the eigenspace of A corresponding to X₁. -5 -9…

A:

Q: Let f: S¹→ S¹ be a homeomorphism.  Prove that h(f) = 0

A: Given that, Let f:S1→S1 be a homeomorphism. Therefore we have to proved that hf=0. So, consider…

Q: prove v(x1) = v(xn) → x1 = xn v injective if x1 xn → v(x1) = v(xn)

A: Injective is another word for one-one.

Q: 100. In a topological space, which of the following statements is correct? Sisianoge (A) a compact…

A: We have to find the correct statement

Q: Question Completion QUESTION B Use Polar Coordinates to find the volume of the given solid. Under…

A:

Q: Output is a function of inputs x1 and x2: y = x₁ 1/4 x2 1/2. Total cost is a function of inputs x₁…

A: Option(2) is true

Q: Define the gradient vector, and explain what it means. Come up with an example you're your own life,…

A: To find- Define the gradient vector and explain what it means. Come up with an example you're your…

Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: 7. (3 tan x 1 - 2 cos y) sec² x dx + tan x sin y dy = 0. ANE cos y tan² y ton3 y L

A:

Q: Corollary 2.53 Let (M, d) be a metric space and KC M. The following statements are equivalent: (i) K…

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

Q: It costs $60 to buy green bean seeds. Green beans sell for $40. It takes 10 days for green beans to…

A: Given The cost of green bean seeds are $60 Green bean selling price is $40 It takes 10 days to grow

Q: 1.use interval notation to determine where f(x)>5. 2.Identify where the local minimum of the…

A: Introduction: A real valued function follows many different characteristics. Increment and…

Q: constrcut green function of  1). wave equation .

A: note :  As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Determine whether the following is true: (a) (b) n+1 Σ₁2²= n · 2n+² + 2, i=1 n i-0 3¹ 1- 3n+1 13…

A:

Q: Calculate the solution of Laplace's equation inside the circle of radius r = 1 with the following…

A: Given That : f(ϕ)=V00<φ<π0π<ϕ<2π where V0 is a constant  To Find : Solution of Laplace…

Q: (2) Give a combinatorial proof of the following: G)-00-0000-00' (i) justify your answer with…

A:

Q: 81) Find the height of a moving box if its length is 32 in, its width is 26 in., and its surface…

A: Let height  = h Length l = 32 in. Width b = 26 in. Given  Surface area of the moving box = 2940 m2…

Q: Find the radius of convergence of the power series n=1 √n Your answer should be a nonnegative real…

A: 1. Given series is ∑n=1∞xnn As if the series is convergent then limn→∞an1n < 1⇒ limn→∞xn12n <…

Q: (b) Starting with the voltage divider rule, show that the power transmission coefficient T of an RC…

A:

Q: The triangle ABC is BC 6.3 cm and AC 7.5 cm. From a point D on AB, a transversal is drawn parallel…

A: For the Given triangle ABC  Length DE= 2.1cm

Q: a) How many second are there in a year? (1 year is 365.15 days) b) A solid piece of copper has a…

A: Given one year is 365.15 days Number of seconds in a day is 24*60*60 = 86400 seconds Number of…

Q: 6. Describe the set of attainable right-hand sides b (in the column space) for b₁ b2 b3 u V = 2 23…

A: 6. To describe: The set of attainable right-hand sides b (in the column space) for 100123uv=b1b2b3…

Q: True or false for M = all 3 by 3 matrices (check addition using an example)? (a) The skew-symmetric…

A:

Q: Determine for which x ER the Taylor series for f(x) equals f(x).

A: Given fx=sinx2   for x∈R

Q: Find the net change in the value of the function between the given inputs. f(x) = 4-5x; from 3 to 5

A: We want to calculate net change in given function from 3 to 5.

Q: (a) Use the method of characteristics to solve the following boundary-value problem: - yur(x, y) =…

A:

Q: Let A and B be compact subspaces of a Hausdorff space X. Prove that AUB and AnB are compact.

A:

Q: The function f(x) is shown in the graph and the function g(x) is defined as g(x) = -7x² – 28x. -8 -7…

A:

Q: Q.6 Solve the Laplace equation U+U = 0 U (0,y)=0,U,(z,y) = 0, U(x,0)=2cos3x+3-2sin²x U(x,1)=…

A:

Q: the differential equation 3(3x^2 + y^2)dx - 2xydy = 0 is homogeneous of what degree? (A) 1 (B) 2 3

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: What is the integrating factor of the differential equation (5æy + 4y2 + 1) dx + (x2 + 2æy) dy = 0?…

A:

Q: a) Using the definition of Laplace transform find L(+²) b) Given the initial value problem 2y" -…

A: (A) To find Lt2 using the Laplace transformation.

Q: ) Consider the vectors -- () --- () --- () a= = Do these vectors form a basis of R³? If yes, prove…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Leanne tries to construct a square inscribed in circle O. She draws diameter AB and then draws two…

A: To draw a square inscribed in a circle.

Q: Set up, in either Cartesia over the region within the cylinder x² + y² evaluate the integral. 2م

A:

Q: The function f(x) is shown in the graph and the function g(x) is defined as g(x) 'y -8 -7 -6 -5 -4…

A:

Q: 1. (a) Given two complex numbers z₁ = 1-√3j and 22 = 1+j, do the following: (i) Plot zi and Z2 in a…

A:

Q: Let A,X EM, (C) such that A is positive semidefinit and AX = XA Show that A¹/2X = XA¹/2.

A: Introduction: Definite matrix is significant in studying quadratic forms. Also, in Lyapunov…

Q: Consider the two functions given below: Function 1: f(x) = -9x² +31x +42 Function II: -50 -40 -30…

A:

Q: Let h(x, y) = x¹ — 4xy² – 2x² + 8y². Find and classify all local extrema of the surface using the…

A: As per the question we are given a bivariate function h(x,y) and we have to find and classify all of…

Q: 5. Let f(x,y) = x² + xy + y² be a function on the domain D = {(x,y) € R²: 24+ y ≤8 and y ≥ 9}. a)…

A: a) Given that fx,y=x2+xy+y2 First, find critical points. fx=2x+yfy=x+2y So,…

Q: Consider the function d: R² × R² → R defined by min{|y2 - x₂, 1} if x₁ = y₁ otherwise, d(x, y) :=…

A: A metric on a set X is defined as a function d: X×X→R which satisfies the following conditions:…

Q: Use zero-through second order Taylor series expansions to predict f(x/5) for f(x)=2sin(x)-cos(x)…

A: Given that fx=2sinx-cosx So, f'x=2cosx+sinxf''x=-2sinx+cosx Now, f0=2sin0-cos0=-1…

Q: 2. Suppose f is holomorphic in an open set UC C and a € U. Show that for any integer n ≥ 0 there is…

A: Given f is a holomorphic in an open set U⊂C. Let a∈U. Now, we form a new holomorphic function…