(b) For each of the following, state and explain whether the equations linear or non – linear, and give its order and degree. d²y i. dx² + k²x = 0 dy i. + xy² = 0 dx d²y + sin(x + y) = sin x dx2

Q: 1+x+y Evaluate 0. dz dy dx 0,

A: see 2nd step

Q: Determine the coordinates of the absolute extremes of y = 3sinx(cosx), 0 ≤ x ≤ 2pi

A: Determine the coordinates of the absolute extremes of y = 3sinx(cosx), 0 ≤ x ≤ 2pi

Q: graph this translation y=2sin2x-3

A:

Q: Evaluate cosh(72) dz, C the line along the imaginary axis from to 2i. cosh(72) dz

A:

Q: Solve the following equation y+ sin r.y sin z.

A:

Q: Find all solutions between 0 and 2n for the following equation:

A:

Q: Solve the following diferential equation (y-y² Inx)dx = xIn xdy.

A: First we reduce the given differential equation into standard form of Bernaulli's equation, then…

Q: Find d²y/dx² for the following equatio: f) x2/3 + y2/3 = 1 g) x³ + y4 = 16

A:

Q: B. Find the x and y of the following equations. 1. (x + jy)² = 5 + j3

A: Solution

Q: Determine whether the equation is linear in the variables x and y.2 sin x − y = 14

A:

Q: y sinx - xy² = C

A:

Q: Determine whether the equation (3x + 2y)dx + (2.x + y)dy = 0 is exact. Find the solution if it is…

A:

Q: Can you evaluate and explain the steps of the following equation

A: Step 1:The integral you've provided is:                          ∫1/sqrt(4 + x2)  dxTo evaluate this…

Q: 1 3. If y=u³ + u²-1, where u = 1-x " dy dx determine Use Leibniz notation .

A:

Q: dy 2) Find for each function: dx a. y= 5x – 7x² - b. y= Jx 1 y С. x² - 5 d. y Зх +1

A:

Q: State the order and determine whether the equation is linear or non-linear. 피(음) + ()' (d²y dy - y =…

A:

Q: 2. (2y? + 2 In x +1) dx +2xydy = 0 %3D

A:

Q: . Solve the first order equation (3z²y + 2ry)dx + (x³ + x² + 2y)dy = 0.

A: Solution

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.