Determine wether the given ODE is exat or not, and find its general solution: (e²y—y cos(xy))dx+ (2xe²y — x cos(xy) + 2y)dy = 0.

Q: Find C1 and C₂ so that y = c₁eª +c₂e¯ª is a solution of the IVP y"−y=0,_y(1)= 0, y′(1) = e

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Q: Utt u(x, 0) ut (x, 0) = = = 4uxx x² + 3x

A: USIND D'ALEMBERT'S SOLUTION FOR ONE DIMENSIONAL HOMOGENOUS WAVE EQUATION ,WE HAVE

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Q: Calculate the exact value of: tan cos Does not exist. √8 1 (G)] 3 3 O2.828427125

A: The given problem is to find the exact value of tan(cos-1(1/3))

Q: Let u₁ = 1, ₂ = 1 and un + 2 = Un +1+uns n 2 1. Then use U2 mathematical induction to show that…

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Q: Consider the following matrices: d₁1 d21 0 0 0 0 d12 d22 0 0 0 0 0 0 C 0 0 0 0 0 e11 e12 e13 0 e21…

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Q: Find the characteristic equation of the given matrix. [8-1 5 2 0 3 1-1 0 0-6-6 0 0 0-5 (8 - A)(3 -…

A: We have to find the characteristic equation of the matrix A where  A=8-152031-100-6-6000-5

Q: Given the first order initial value problem, choose all correct answers dy 2x-3y y(-1)=2 dr 4y + 3x…

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Q: A rectangular lot is to be enclosed with two types of fence. Two opposite sides must receive a…

A: It is given that the rectangular plot is to be enclosed with two types of fence. Let x be the length…

Q: 1000 Let A = P = -6 -4 12 -1 -3 3 -2 -2 4 Find an invertible matrix P and a diagonal matrix D such…

A: Solution is below -: Firstly we have to show that matrix is diagonalizable then using the definition…

Q: For each of the following functions de R²X R² [op) Say whether a is a medruc. Briefly explain your…

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Q: Determine whether the following statements are true or false a. Vector v exists in the kernel matrix…

A: (a) Vector v exists in the kernel matrix A if Av=0 Ans: True Explanation:KerA=v: Av=0 (b) The kernel…

Q: IUT Problem ? (2 points). Give an explicit example of a homeomorphism. f: [0,1] → [0, 2].

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Q: BESTEMMARHAN AHLIMMERNISS Find each of the following. Write answer as a reduced fraction. The…

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Q: Let S = {1, x, x²} be a subset of the vector space P(C) equipped with the inner product 1) = [₁, f…

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Q: Using the principle of mathematical induction, prove that (2n − 1) 3¹ +¹ + 3 - 4 1x3+2x3²+3 x 3³…

A: The given problem is to prove the following identity by using the principal of mathematical…

Q: 13. Is the sequence {a} a solution of the recurrence relation an = 8an-1-16a₁-2 if a) a₁ = 0? c) a₁…

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Q: Find y(t) solution of the initial value problem y"+y'-20y=7δ(t-2), y(0)=2, y'(0)=3 where δ(t) is the…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: a. b. d²y dt² d²y dt² +4y= cos2t y(0)=-2 and y'(0) = 0 dy + 5y = 2ety(0) = 3 and y'(0) = 1 dt

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Q: For each of the following functions diR² AR²" wether I is a metric. Briefly explain [0,00) say…

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Q: For nists of integers, provide mula or rule that generates the terms of quence that begins with the…

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Q: Let u = ·[³]. and v = Select all of the vectors that are in the linear combinations of (u, v).…

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Q: You purchased a car for $30 000. It depreciates by 25% of its current value every year. a) Write a…

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Q: Find the area between the graph of y-5-5x^(2/3) and x-axis and −1≤ x ≤ 8 using the right hand rule…

A: Given Data: Let us consider the given function is, f(x)=5-5x2/3. To Find: Area between the above…

Q: Prove that if p and q are distinct odd primes, then we have (p-1)(q-1) 4 25 52 TID = (-1) quadratic…

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Q: Problem (4 points). For each of the following functions d: R2 x R² → [0, ∞), say whether d is a…

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Q: Find the determinant of the following matrix using the co-factor expansion method. -1 2-2 -3 1 1 -3…

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Q: I'm let na 1 mem memy be and & 1 (n) be non-Mar function, we have,

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Q: Find the surface area generated by rotating the given curve about the y-axis. x = ett, y = 4et/2, y…

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Q: 1. Let S = {₁, 2, 3, 4, 5, 6, 7} be the set of 7 distinct integers. Use the Pigeonhole Principle to…

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Q: A line makes angles a, ß, y and with the diagonals of a cube cos²a + cos² B+ cos² y + cos²8= 4/3.

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Q: (88) Write a nonzero vector in span (S) that is not equal to any of the vectors in S.

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Q: 4. Trace the curve: y² = x²-4x-12 x²-2x-3

A: y2=x2-4x-12x2-2x-3

Q: 20. then X(x) and T(t) are respectively solutions of If X(x) T(t) is a nonzero solution of the…

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Q: Consider the function f(x) = = −1, X, 1, −2 < x < −1, −1 ≤ x < 1, 1 ≤ x < 2. (a) Sketch the graph of…

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Q: 1. Find the value of k so that the ODE (y³ + kxy¹ − 2x) dx + (3xy² + 20x²y³)dy = 0..

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Q: A committee of five people is to be chosen at random from a club with 13 members comprised of five…

A: Given: Total members=13            Total men=5             Total women=8To find: The probability…

Q: 12 Let u₁ = 1, ₂ = 1 and un + 2 = Un + 1 + un n ≥ 1. Then use mathematical induction to show that 1…

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Q: x' + 4x = 108 (1-2) Initial Conditions: x(0) = 1, x'(0) = 5 8 (t) = the Diract Delta Function Find…

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Q: Expand f(z) 0<=<4 2-6 4<2<8 in a Fourier series of period 8.

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Q: d. 25 +3 52+5+1 b. उ 3 5°4 25 +bs

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Q: Let f. ROR be a Continuous function with f(x) ≤ 10 for = all XER. Explain why f is not homeomorphism

A: A homeomorphism is a continuous bijection with continuous inverse.

Q: Compute the determinant of the matrix by cofactor expansion. -3 2-2 2 0 -1 2-2 0 3 0 -3 O 0 90 -90…

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Q: Prove algebraically that  A+A'B'=A+B'

A: We have to prove algebraically that  A + A'B' = A + B' We know that, the distributive property  A +…

Q: Fill in the blanks by converting between percents, decimals, and fractions. If needed, round…

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Q: Find the values of p so that line 1-x_7y-14 z-3 = 2p 2 3 and 7-7x_y-5_ = 3p y75 = 6 1 -5 6-z 5 are…

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Q: F = y² = y) + 3z²k C: The ellipse in which the plane 2x+6y3z - 6 meets the cylinder x² + y²1,…

A: The given problem is to find the circulation of the given vector field around the given curve by…

Q: (b) For ($(t) = (ýdı yöu). let y^² = 4²" + c₂us →di y" (0) = (6) >> So you = ( 2 Sintl) + (os (t)…

A: The columns of the fundamental matrix are the solution if the system X'=AX.

Q: Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation for…

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Q: . Find the general solution of the third-order ODE y(4) — 5y(³) + 6y″ + 4y′ − 8y = 0, note that m² −…

A: Given the third order ordinary differential equation, y4-5y3+6y''+4y'-8y=0. To find the general…