Consider the differential equation 12x²y" + 23xy' + (12x² - 1) y = 0. Determine the indicial equation using the variable r. 12 r² + 11 r −1 0 ✓ Find the recurrence relation. (-1)-1.12n-1 an i = (r+n) (12 (r+ n − 1 +23) − 1) - Find the roots of the indicial relation., Number of roots: two 71 = X DO n=1 1 12 an-2 for n = 2, 3, ... 72 = Find the series solution (x > 0) corresponding to the larger root. (-1)"62 y₁(x) = x21+ n! 37. 61 (24n+13) -1 ✓

Q: By using fixed point approach solve the Value of A=√√20 A = √√² + √2 + √2+..

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

Q: CK Show whye* dx does or does not converge.

A:

Q: 5. x' = (1²3) × X 5

A:

Q: 2. Let T : R³ → R³ be the operator given by -1 1 0 0 −1 1 0 0 – 1 - T(v) = = v. Determine whether T…

A: given matrix T=-1100-1100-1 determine whether it is decomposable or indecomposable.

Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

A:

Q: General Solutions and Phase Portraits. In each of Problems 1 through 6, find the general solution of…

A:

Q: Find an equation of the plane tangent and an equation of the line normal to the surface 7z = 4x² -…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Point G is the circumcenter of AABC. Find the following measure. G 11 GB= 0 F B E

A: Given: The point G is circumcenter of ∆ABC. To find: The measure of GB and GD.

Q: 2. Consider the integral [² which can be computed exactly. a) Apply Romberg integration to estimate…

A:

Q: General Solutions and Phase Portraits. In each of Problems 1 through 6, find the general solution of…

A: We are given the system x'=5434-34-14x So, the matrix of coefficients is A=5434-34-14 Firstly, we…

Q: 4. At which points does the function f have absolute maximum or minimum, or local maximum or…

A:

Q: Using quadratic interpolation find In 9.2 from In 8.0-2.0794, In 9.0-2.1972 and In9.5=2.2513.

A:

Q: 1л 4 X Оп = 0 = 0.7853 Іл 2 Зл 4 п = 3.1416 = 1.5707 = 2.3561 f(x)= sen (2x) f(0п) = sen(2x0) = 0…

A: To Sketch: The graph of f(x)=sin(2x) for the given values in the table.

Q: b) Sketch the graph and find the points on the cardioid r=a(1+cos) at which tangent lines are…

A: Consider the equation of the cardioid, r=a1+cosθ The graph will be,

Q: a) 2-3u(t-5) cost = -t Find the 33 Ordine Lap of

A: The given function is ht=-t cos5t-3ut-5cost To find: the Laplace transform of the given function.

Q: Using Fermat's little theorem, find the solutions of the following linear congruences. a) 7x ≡ 12…

A: Fermat's theorem :  Let p be prime number such that gcd(a,p)=1 then ap-1≡1(mod p) Using Fermat's…

Q: Consider a differentiable function g where g(6, 8) = 2, g(6.5,8) g(6, 8.25) = -1. = 5 and A.…

A:

Q: AX=B 10 18.5 37-1 18.5 37.1 78.8 174.9 37.1 [A, B] до 78-8 I al a2 $2.6 = -14.0 -63.2 -63 10 18.5…

A:

Q: 3. Apply Lagrange's interpolation formula, find In 9.2 with n=3 and the values below 9.5 10.0 11.0…

A: To find- Apply Lagrange's interpolation formula, find ln 9.2 with n = 3 and the values below X…

Q: 3. *- ( 7 ) x + ( ) X =

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Q.4: Find the third order Lagrange interpolation polynomial using the following table to compute…

A:

Q: (a) Suppose the functions f and g are continuous on [a, b], differentiable on (a, b), and g'(x)0 for…

A: For 1st part we will use ROLLE'S THEOREM Suppose f(x) is a real valued function in the closed…

Q: Find a particular solution to the differential equation using the Method of Undetermined…

A: the given differential equation is                                  x''(t)-10x'(t)+25x(t)=138t2e5t…

Q: An anchor chain is wound around a drum with radius 1.5 ft. If the Drum is rotated through an angle…

A: It is known that a full rotation around a circle is equivalent to 2π or 3600. The perimeter of a…

Q: 2. Consider the integral ² sir sin redr which can be computed exactly. a) Apply Romberg integration…

A:

Q: A rectangular tank with a square bottom has base side lengths of 3 feet and a height of 10 feet is…

A: Given that the base of the tank is a square and shape of the tank is rectangular. Also base side…

Q: The first three nonzero terms of the Taylor series for f(x) = cos x centered at a = π are (x-1)³…

A: Sol:- Taylor series of function fx at a is defined as: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…

Q: ebook from the office store pent $8.25. He went back t ext day and bought two mo iders and three…

A: # As per the guidelines we are entitled to solve one question at a time please resubmit the other…

Q: Approximate the area under the curve y=x^2 from x=2 to x=4 using a Right Endpoint approximation with…

A: Right Riemann Sum formula ∫abf(x)dx≈∆xf(x1)+f(x2)+f(x3)+...............+f(xn-1)+f(xn) where ∆x=b-an…

Q: Determine the form of a particular solution for the differential equation. Do not solve. y"-y=te 7t…

A: Given equation is y''-y=t e7t+6t2 e7t   To determine: The form of a particular solution for the…

Q: What is the area of this figure?

A: The trick here is to divide the figure into known figures like rectangles, squares, triangles.

Q: 3) Convert the following triple integrals to cylindrical coordinates or spherical coordinates (do…

A:

Q: 2. Consider the following vector 1 v= = [1, 0, √6 (a) Write a projection on this vector. Proof your…

A:

Q: has its largest value. a = Find two numbers a and b with a ≤ b such that b= # # L (6-52 (6-5x-x²)…

A: Given integral is ∫ab6−5x−x213dx. We have to find the value of a and b with a≤b. The integral…

Q: Consider following t= 7 pi/3 Find reference number value of t Find the terminal point (x,y) of t

A: Reference number value is π/3 Terminal point is (0.991,0.127)

Q: Q.5: Find a power series solution of the differential equation, a (0.3); where the initial values,…

A: y''-y=0 Let y=∑n=0∞anxn be power series solution

Q: 3. In the plane R², consider the parametric curve given by the equations [x(t) = cos(t) + 2 [y(t) =…

A:

Q: QUESTION 13 Is this true or false? The radius of convergence for 00 ΣΕ" n=0 is R = Show why your…

A:

Q: In Exercises 15-18, find the values of k for which the matrix A is invertible. 15. A k-3 17. A = 3…

A:

Q: All polynomial expressions should be written in (5) form, meaning that the terms are placed in (6)…

A: To find- Complete the sentence.  All polynomial expressions should be written in 5…

Q: Solve the differential equation by variation of pa 2y" - 4y + 4y = ex sec x y(x) =

A:

Q: Clearly illustrate with explanations why lim 10D *→00 80,012 #100

A: We have to show that limx→∞x100e0.01x≠100 We can see that limx→∞x100e0.01x is of the form ∞∞ Apply…

Q: 1=₁x-e³dx Obtain the numerical integral of the integral by dividing the integral into 5 equal parts…

A: Given: I=∫36x·e3xdxWe have to evaluate the integral using the Trapezoidal method and Simpson's…

Q: Q1:A/ The Office Supplies Company offers two types of pens, the first type has high specifications,…

A: Since you have posted a multiple question according to guildlines I will solve first (Q1.A)question…

Q: solve the following linear programming problem using graphical method Min (z) = 300x₁+200x2 S.T.…

A: Min(z)=300x1+200x2S.T.20x1+20x2≥16030x1+10x2≥120x1≥0, x2≥0 We have to solve using graphical method

Q: Consider the function i) f(t) = For r. MICHAL a half-ranc 0 <1 < 1/12 1 <1<1 function, f(t)rier co…

A:

Q: Find the steady state matrix X of the absorbing Markov chain with matrix of transition probabilities…

A:

Q: Consider the following differential equation. 3x2y" + 2xy + 9x²y = 0 (c) Find the series solution (x…

A:

Q: Compute lim by following these steps lim Missing steps A lim 87 XXIN Missing steps B What do you…

A: limx→∞ex+2xex+5x

Q: Given a system of differential equations i) dx dy + dt dt 2 Filho dx dt Show that +x=3√ue™ du which…

A: We have to show that Ys=2s+12s2-2s-1 Then we can proceed further.