3. Solve for the solution of the following Higher Order Homogeneous Diff Eq and determine the nature of the roots: a. (2D5 - 3D + 2x² +6)y=0 b. (D2-8D+17)y = 0

Q: a. Show that If 1 iv3 z = 2 2 Then z7 = z. b. Evaluate all the roots of the Equation: z* + 16 = 0

A: We will solve both the parts only using some basic knowledge of complex numbers and their…

Q: Use the quadratic formula to find the roots following quadratic: y = x² + 4x +5

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Q: If the sum of the roots of the equation 1/(x+ a) + 1/(x + b) = 1/c is zero, then prove that the…

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Q: Find all solutions of:2x + 2y + 4z = 8x - y + 2z = 2-x + 5y - 2z + 2

A: First we describe the given equations as a matrix. And then we use Linear algebra to solve the given…

Q: 3. Find the intersection of ₁ and ₂: ₁2+ 4y-32= -9 ₂: 4r +9y+2z=-1

A: Given planes equations:- π1: x+4y-3z=-9π2: 4x+9y+2z=-1

Q: Put the equation y = x + 6x + 5 into the form y = (x - h)' + k: Answer: y =

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Q: Determine all solutions. y = xy² - √x² + y²7

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Q: 2D4-4D³-23D² + 12D + 36 = 0

A: Given auxiliary equation is 2D4-4D3-23D2+12D+36=0 Now we replace D by x f(x)=2x4-4x3-23x2+12x+36…

Q: Solve when x(0)=2 and y(0)=3

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Q: Solve 2 2 |

A: Proceed as shown

Q: Calculate  x and y (2+xi)+(y+3i)=7+4i

A: Complex numbers are those numbers which is represented in the form of (a + ib) where is a real part…

Q: 1. (4 X6 x) +62 = 1

A: These are the problems of the theory of congruence.

Q: Solve (mz-ny)p+(nx-lz)q=ly-mx

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Q: 1. (4 ×6 x) +6 2 = 1 2. (3 x6 x) +65 = 1

A: These are the problems of the theory of congruence.

Q: Which of the following quadratic equations has the sum of product of the roots to be 4 and 7,…

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