For atims (3) to (8) refer to the À = x2i + (2x"-y)j - yzk and = 3x²y + y² z? followning = X? %3D (3) ♡ Ø (4) D.A

Q: Find y (2) if D.E. 2 dx +3y=sin 2x₁ y(0) = 6

A:

Q: b. (3x2 – 2y²)y' = 2xy; when x = 0, y = -1. Note: use y = XV

A: We need to solve differential equation.

Q: S (5x - 3x + 5) dx %3D

A: recall: ∫xndx=xn+1n+1+C

Q: ddy if y= (x² + 4x)² dx Simplify completely. Do not multiply out any binomials raised to more than…

A: y=Rules(i) (ii)  (iii)

Q: y - 1 %3DCOS (7x*) dy dx %3D

A:

Q: d (7) Vtan²s+ 21 dt = dx

A: Explanation of the answer is as follows

Q: Find ∫√(2x − 1) dx.

A: Given:

Q: Differentiate. y= In [(x +2)° (x + 5 (x+ 7)°] [In [x+ 2)° (x +5)*(x + 7) ]] =O dx

A:

Q: 3.2 (2x - y²) dxdy

A:

Q: c) Evaluate [| 4xy where D is the portion of x + y = 2 in the 1* quadrant.

A:

Q: Consider generalizing in the following way: N customers line up for their sandwiches, and you are…

A: The probability of an event is the chances of happening of the event. It can be defined as the ratio…

Q: (х + 2у — 4)dx — (2х + у — 5)dy %3D 0

A:

Q: V3/2 1 dx%3D 6). V1- x 1/2

A:

Q: Find dy. 3 y=³√√x (6-5x).

A: Given query is to find differential.

Q: Find if x = and y = t +3 (t+1) 1 %3D dz O a. none of these O b. (t+1)°(4t + 3) Oc름(t-1)°(4t-1) O d.…

A:

Q: dy +Zy =0 du

A: Given: dydx+2y=0   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx, where 'a' is the constant.…

Q: II. Evaluate the following. 1. 2x+4x-3 dk 2. Sx-8 x-2 3. J vx*-2x'+x*dx

A:

Q: find dy. y =2√x/3(1 + √x)

A: we have to find the derivative y=2x3(1+x)

Q: a) Integrate the following functions i. (-2x² – 9x – 7)dx (4x* – 9)* (20x“ )dx. [-4e"dx ii. iii.

A:

Q: 8. (2x° – 3x) dx

A:

Q: Evaluate. 1 -2 (6x +y) dx dy 0 -5 1 -2 | (6x + y) dx dy =(Simplify your answer.) %3D 0-5

A:

Q: 1 0 2x² - 1 x- 3x + 15 dx

A: Numerical integrations such as Trapezoidal Rule, Simpson's 13 rule, Simpson's 38 rule etc. can be…

Q: Evaluate Set 7x cos (6x) dx. Sex cos (6x) dx =

A:

Q: 1/3 + 4y/6 = 2/3 Show your work

A: The given equation is 13+4y6=23To solve for the value of y

Q: dr Find if r (x) = 9x 2 + 5x – 3. dx

A: Given,            r(x) = 9x2 + 5x - 3

Q: Find y". y = x(3x + 2)*

A:

Q: .5 X° +2x -Xp- X +1 -3 X° + 2x -dx%(Simplify your answer.) %3D X +1 3.

A: Consider the integral

Q: (2e20 4e* – 1)ž 2 -

A:

Q: 9 4 2 10x²¹² + 3 dx √x

A:

Q: | (b) b)5zVE+z-/2 dx.

A: To evaluate the given integral

Q: Let y = (3x²-2)* (4x + 3)7. %3D Find y'.

A:

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.