Suppose we want to show a classmate the basics of how to integrate with the u-substitution technique. Which of these examples will be the best one to share with the classmate, to demonstrate the basics of u-substitution S (sin z)° - tan z dx S sin x dx sin = + dx S (sin x)* - cos z dx

Q: To obtain the General Solution of si What will be the form by separation of variables? cosv A)…

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Q: B.S(cos x + cos 5x)dx D.S(cos x – cos 5x)dx A.S(sin x + sin 5x)dx C.S(sin x – sin 5x)dx 8. S sec³x…

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Q: Evaluate [[ sin(y²)dydx where 2: 0<y<1, 0<x<y°. 0 x b) a-cos¢x)) (1 a) 1-cos(x) 1 - cos(1) c) 2 d)…

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: Given: a = 0 – sin 0; y= 1- cos 0 d'y Find: dz2 O d'y 1 dz2 (1-cos 0) d'y 1 %3D dz2 (1-cos 0) O dy 1…

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Q: What is general solution of the given ODE. * dy = cos² (x − y + 1) dx cot (x-y+1) + x + 1 = C Option…

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Q: Is the ODE (sin(x-y)+1)dx=(sin(x-y)-2y)dy satisfied by the implicit solution x+y2=cos(x-y). Show…

A: An implicit function, however, is an equation that defines a relationship between two or more…

Q: 5 dr dy Suppose x and y are functions of a third variable t. If sin²(x) + cos²(y)=- and dr - 2, what…

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Q: B: By using Homogenous method solve the first order differentia еquation (1+ e») dx - e"l> -1) dy =…

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Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…

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Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: dy/dx = sin2xsecy for x∈ (-π/2, π /2) considering y equals π/6 at x equals π/6 & (cosx)dy/dx +…

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Q: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]³dx gettyimages FUsC When:x = 0; y…

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Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

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Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Evaluate ∫2x4x2-1dx          ...(1)

Q: Find the general solution to 2- ди u = xt + x cos t + t sin x. 3 - -

A: Given: 2∂u∂t-3∂u∂x-u=xt+x cos t+t sin x

Q: 2. Evaluate: S(cos x)(In sin x)dx A. sin x (1 – In sin x) + C C. sin x(In sin x – 1)

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Q: cosxdx 17. secx+ tan x 18. [2sin(3x)cos(5x)dx 19. [(sin y + 2 cos y)'dy 20. ſcot'(2x)dx 21. [sin“…

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Q: (4,0,2) S sin y cos x dx + cos y sin x dy + 3 dz (1,0,0)

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Q: 2(1-z) Evaluate S-" ==-2) dy dx dz

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: 2,3 Given z = sin (x + y) where x = s²t, y 2s 3t. az as az at

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Q: The general solution of y"+ 16y=cost is: Select one: a. y = C,cos(4t)+ C,sin(4t) + 1 cost 15 b. y=…

A: Here I am attaching image so that you understand each and every step.

Q: 9-x 4. Evaluate ſ, S sin(x² + y²) dy dx

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Q: Solve: (2y cos x +sin x) dx = sin r dy O y csc r CoS 7 = ( O y sec a + sin r = C Oy csc a+ cos r Ov…

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Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]*dx gettyimages When:x= 0;y =, %3D

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Q: 18) * x-sin 2x ; find y" y y" cos 2x y = 7 %3D Option 3 O Option 1 y" sin 2x

A: First we find out first derivative with respect to x then we find out 2nd derivative with respect to…

Q: What happens if you can write a function as a composite in differentways? Do you get the same…

A: 39. Part a). It is given that, y=cos u and u=6x+2 Therefore, dydu=-sin u  and  dudx=6 So,…

Q: $5. (i) show that: sin 0+sin 20 = tan 0 1+cos 0+cos 20 (ii)Find the general solution of the equation…

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Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

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Q: What is the general solution of sin x sin ydx + cos xcosydy = 0 O tan x = O sin x O sin y + cos x +…

A: To solve the given differential equation.

Q: Find the general solution of (cos cos y +ycos x ) dx + (sin sin x – x sin sin y ) dy = 0

A: The given differential equation is incorrect and hence the correct differential equation is as…

Q: If z = 24 - 2x - 6y, x = cos(4t), and y = esint, then dz dt is equal to O-2 sin(4t) - 6esint cost O…

A: Since you have posted multiple problems we will answer first problem for you for remaining problem…

Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: If y = x² + sin(xy) find y' 2x+y cos ry 2y-x cos ry 2x+x cos ry y-æsiny 2x+y x cos ry x-y sin æ 2y…

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Q: 35. Given that d = 6(sin 2x - cos 3x) and y = 0 dx when x = 0, y = A -3 cos 2x - 2 sin 3x – 3 B 3…

A: We can solve this problem using initial value problem.

Q: The value that will satisfy potentia. function p is x + y sin x None = In (x +y %3D

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Show that y = sin x, y = cos x, and y = a cos x + b sin x (aand b constants) all satisfy the…

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Q: Find y, of 2 -3+2y 6 cos x+9 sin x dx ... a.) y, = 3 cos x+ 2 sin x b.) y, = 3 coS x- 2 sin x c.) y,…

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Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]*dx gettyimages Fuse When:x = 0; y…

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Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

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Q: (8 cos x cos y + 4 sin x sin 2y + 1) dx – 8(sin x sin y + cos x cos 2 2y) dy = 0

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

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Q: [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]³ dx gettyimages When:x= 0; y = 2

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: 6. x sec x tan x dx

A: Let's find.

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

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