(i) (z+ yx)(x+ yx)(xy+xZ)(z+y)

Q: 4 r°tan|r (r*)dr 4 5+3 ln cos (r

A:

Q: dx J (x² + 2x – 10)²

A:

Q: 3y3 (2y+3) (y-5)

A: The given expression is

Q: If y = 5(1 - e-2x), compute y and show that y = 10 - 2y.

A: To compute y'

Q: 3(y-2) 1- 3y

A:

Q: 2x + 1 (b) √ ² (1 − x) -dx

A:

Q: (2x)(x-y+5)(5y)

A: Firstly, we multiply 2x by each term of x-y+5

Q: (c) Write (V3+ i)" in the form of x+ iy.

A: Here I have applied De Moivre's Theorem. See the solution.

Q: Solve (D4 + 2D² + 1)y x cosx +3*

A:

Q: (x - 3 bxy + 2 b?y?) (xdx + ydy) = xdy-ydx %3D

A:

Q: y = (1– 2x) ;y" ¡y"

A:

Q: D2 – 5D +6)y=3xex+2x2 , y(0)=0,y,(0)=1

A: Given differential equation is homogeneous ordinary differential equation. To solve this equation…

Q: factorise (c) x - - 3x - 4x + 12 (f) x'y – 4xy

A:

Q: Differentiate y = 21/2 4 - x (4 – x³)'"2 -

A:

Q: is f(x) = -3x + 4 a bijection?

A:

Q: e) Solve [(-x'y)² + (x²y)³]²

A:

Q: Eliminate the arbitrary constant. y=Ax² + Bx³ 7xy "-x²y + 15y = 0 A (В) B (C) D x²y-7xy "+ 15y = 0…

A:

Q: S,(2x-y)dxdydz

A: Consider the integral: ∫12∫0z2∫0y-z2x-ydxdydz

Q: 3x- 2 6. y(x)= X -1 y (x) = (x-1)?

A:

Q: (x + 2)³ y = (x² – 4) ||

A: a2-b2 =(a-b)(a+b)

Q: xy – 3y + 3x² – 9x =

A:

Q: (d) (* + y, x - v)

A: We have given a vector field (x+y,x-y) with four diagrams;

Q: y(4)-8y" + 16y=0

A: To solve the differential equation