Find a solution x, y E Z to the following diophantine equation: x² +y•x+ 3 · y? = 851. Your answer should be an ordered pair [x, y] in between square brackets consisting of the solution found (e.g. [x1.y1]). 1+v-11 Note that Z[ ] is a Unique Factorization Domain.

Q: 4-a. For the equation: (1–i)x+2i (2+3i)y+i + 3+i 3-i find the real value of x.

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Q: — 16х + 3 Evaluate J = dx. x - 20x + 101 2 J = (Use C as the arbitrary constant.)

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Q: 2. Write the given equation below in standard form. 4x2 + 3y + 6y = 9 (y+1)? =D1 *+ (y+1)? = 1…

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Q: 2. Homogenous DE x²y = 4x2 + 7xy+ 2y²

A: We solve the given homogeneous differential equation

Q: Solve by completing the square: (y-3)-(y-4)(y+3) O A. 1-10,1+Vi0 O B. 1-i10,1+i10 O C. 1-2i2,1+ 2i2…

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Q: ĉu ôu = 0 using the transformations v = .x + y,z = 2.x – y Solve: B.

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Q: Solve for y. 2y² + 7y−13= (y+ 1)² If there is more than one solution, separate them with commas. y =…

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Q: 1. Given a line P(t) through the points Po = [1,0|7 and P [2,4]7 in 2D (a) Extend P(t) to…

A: The problem is concerned with projective plane , line and homogeneous coordinates

Q: Find a general solution. y₁ = y₁ + 2y2 + e²t Y2 = -32 +42e-2t NOTE: Write arbitrary constants as c₁,…

A: Linear differential equation  where  are functions of x or constants.Then Integrating factor (I.F.)=…

Q: Determine whether y, = 3e2t – e-3t and yz = 2e-3t – 6e2t form a fundamental set of solutions. HOW…

A: We have to determine whether the given set of solutions y1 and y2 form a  fundamental set of…

Q: ) Find the points of intersection between −4x − 8y = 2 and 2x = 8 − 4y. b) Find the points of…

A: Intersection of two lines

Q: Find the change of variable x = Py that transforms the quadratic form x' Ax into y' Dy as shown. 2 −…

A: Matrix A is of quadratic form ( from LHS) and D be diagonal matrix of eigen values (from RHS)…

Q: Can you help me step by step with this problem?

A: Obtain the first derivative of the given function as follows.

Q: Solve the rational equation: 8. 3. 3x + 22 | X - 2 x + 1 х - х-2

A: The objective is to solve the rational equation.

Q: S 10х T U бх + 3

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Q: Q1. Solve the following first order equations: (a) (r²y² + 1)dx + 2x²dy = 0, use the substitution ry…

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Q: y" – y = 2xe". Y' %3D

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Q: Eliminate the arbitrary constants A and B: y = Ae-2x + Be³x

A: We have to solve

Q: 17. The height, h, in feet above the ground of a person riding a Ferris wheel can be modeled with…

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Q: Match the correct angle measurement with its letter from the diagr c° 42° bo do <C [ Choose ] <b […

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Q: solve the following equations below?

A: 11. subtract 2x2-9 from 5x2+x+912. y=-x2+2x-4

Q: J (4) (10y + 60) o (2x) find x (3x-20) find y

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Q: (a) (2x+5y=-4 (Use Elimination-by-Addition.) 13x-2y-13 [y 1-3-2x (b) (y=x² (Use Substitution.)

A: Solve for (x, y) as indicated; use ordered pairs in the answers (see attached)

Q: Consider the following equation: 10r + 3y = - 18 A) Write the above equation in the formy = mx + b.…

A: Given equation, 10x+3y= -18

Q: x2 - 4ху- 2у2-2 %3D0 4xy to

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Q: 5 Solve for both x and y in ABCD. X = y= A B (3x - 32)° 4yº (y + 87)° D 2x C

A: fro properties we know that (3x-32)°=2x°  and  (y+87)°=4y°

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.