Which of the following characteristic equations is primitive ? Select one: а. х3 + 1 b. х3 +х+ 1 С. ХЗ + x2 +х d. x³ + x² + x + 1

Q: Find the general solution to the yiven Euler x* j -3xy = 2.

A: Given differential equation is x^2y" - 3xy' + 9y = 0

Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

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Q: Write down the characteristic equation and find the general solution to x'' - x' - 2x = 0.

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Q: Show that under the transformation: k= the equally spaced z-values, z : 1o, To +h, xo +2h, .…

A: Just substitute the given values of x and proof will follow.

Q: The convolution of e2t ® sin(3t) S is | e2Usin(3t – 3u)du e2usin(3t – 3u)du Se-2usin(30)du…

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Q: ) Compute the four 4th roots of −T + Ti where T=7

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Q: 7 Σ (4-J) J=3   (Find Sn)

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Q: A student is solving a Cauchy-Euler equation and writes the following auxiliary (characteristic)…

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Q: 1 find a- w = +y b- w = tan-¹2 az w a²w ах дуа

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Q: Find the general solution of the ODE. y" +9y = 6 cot²3x

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Q: Prove that the equation ! + = 1 has no solutions in positive integers æ, y, z.

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Q: 3. Theorem ZG =. 101 H

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Q: 2. Solve the given SLE using LU-Factorization X, + Xz +Xz = 3 X, - x, + 4x, = 4 2x, +3x, -5х, -D0

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Q: Solve the PDE u + 2xtu,=u²; *ER,t> 0 by reducing it to an ODE using an appropriate choice of…

A: As per the question we are given the following first order PDE : ut + 2xtut = u2  ,  x ∈ R , t >…

Q: Find the imaginary component of In(2z + w) if z = 11 + 9i and w=10+4i .

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Q: 2, z) = 5 and the surfac e at (1,2,3). Evaluate = reasons).

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Q: Find all the values of In(4 – 4j). What is its principal value?

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Q: A student is solving a Cauchy-Euler equation and writes the following auxiliary (characteristic)…

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Q: Find v' ( + 2) dt. Show the computations that lead to your answer.

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Q: 2) Use completing the square to find the following: s+4 а) L-1 ans: e-2t cos2t + e¬2tsin2t (s²+4S+8)…

A: We have to answer the following... a. L-1s+4s2+4s+8b. L-12ss2+12

Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

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Q: Calculate the value of 1n(-V5 – V5i )

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Q: 6. Show that (1) Cou(B1, g) = 0 (2) Cov(3o, B1) %3D

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Q: Find the value of m that makes: Show that the equation  xex-1=0 has a unique solution on [0,1].

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Q: Find all values of z such that cosz = 4.

A: We find all values of z such that cos(z)=4

Q: 2. Solve the given SLE using LU-Factorization X, + x, +xz = 3 x, - x, +4x; = 4 2х, + 3x, — 5х, %3D0…

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Q: 3. Theorem ZA = ZB 101C E 68 D

A: The sum of the opposite angles in a cyclic quadrilateral is 180o.

Q: the following DE are Bernouli type and solve: 1. y’ – x = y 2. y’ + 5y/x = x 7 y 4

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Q: 11T 60. Given that sec 12 13T V2 - V6, determine the value of sec 12

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Q: Which of these best describes T?

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Q: :Use inverse matsix (by Gauss Jordan an Elimination) to solve the syálem 2x + By +3 = - 1 %3D 2x…

A: Consider the given equations 2x+3y+z=-13x+3y+z=12x+4y+z=-2 The given equation can be written as AX=B…

Q: Prove that the equation * + + = 1 has no solutions in positive integers x , Y, Z.

A: x/y + y/z + z/x = 1 if x , y , z are positive integers then case 1 :  If all three numbers are…

Q: The ODE z dr - 3y = 0 is a Cauchy-Euler equation and has one solution of the form y =r" for some…

A: The given statement is true.

Q: Which of the following DEs are first order linear DEs?

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Q: R. find he Corficient of

A: We need to find coeffiient.

Q: Suppose three similar geometric figures are constructed off the three sides of a right triangle in…

A: Consider a right triangle with the length of the altitude a, the length of the base b and the length…

Q: Find all the joint moments m,1, n and k= 0, 1. . .

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Q: Find the F.T. of the following-peridic signal -2 2.

A: From the given graph  periodic function is fx=1-x, 0≤x≤1 with period 1,

Q: et §, ŋ, o be real numbers and consider ctors (1,5,§³); (1,ŋ,n³); (1,0,0²). Determine e conditions…

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Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

Q: 14. Substituting appropriate values for x and y into the formula of Theorem 9, show that (a) = 2";…

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Q: a. Let z1 = 2 – 3i, z2 = 3 + 4i and z3 = 1– V3i. Find z1z2 + z3 then sketch it on Argand diagram.

A: Simplify Z1Z2 + Z3 in simplest form and convert it into polar co-ordinates.

Q: - How many modes does X have?

A: The probability function of X can be described as X 1  5 10 15 f(x) 24k 100k 150k 150k

Q: How many distinct values can z = i^(3i) take on?

A: Given is a complex number  z=i3i. We need to find the other distinct values for z.

Q: 2. find the the following equation in simplest arbi Saution set of form. X-3x + 9 = 5Y-10

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Q: Find the general solution of the given ODE * 3x+2y

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Q: If z = 1+ eie Find z*, z?.

A: Conjugate of a complex numberz is formed of same real part and opposite imaginary part. Its…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.