(D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx + = sinx Yp = COSX +-sinx d. y, =cosx +sinx 5.

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: 1. (xy' – y) cos ( 2у COS -3x4

A: Since you have asked multiple questions, we will answer the first question. If you need answer for…

Q: (a) [(0.6e15 + 4t 3t² +03-10-01 at 4t4-3t3 + 0.3 _10t 1.5 -0.1 2t3 (b) Evaluate…

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Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

Q: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Solve for the first-order DE: y’+y-y^2(cos2x-sin2x)=0

A: Solution: A first-order Bernoulli ODE has the form of y' + p(x)y =q(x)yn Rewrite the form of…

Q: If cos(4x – y) = x+y, then dx A -1 - sin(4x – y) 2+4 sin(4x-y) (B) sin(4x-y) 1 1+sin(4x-y) C) 1+4…

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Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

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Q: y = (sin x +cos x) sec x = sec² x

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Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

A: Given 3x2-y2=t2 and y=tsinθ

Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

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Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

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Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

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Q: / – 9x* sin²(7y") = 9x* cos²(7y/") What is y(4) if y(0) = 8? %3D %3D

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

A: solution is given below

Q: Find d-/dx² at the given point without eliminating the parameter. x=0+ cos0 and y=1+sin0 ; 0 =a/6,

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Q: y=cos(4x) /cos22x-4sin2x cos2x differentiate?

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Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

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Q: . у" — 8y' + 16у %3D е 2x sin 4x + 2e4x + 5х

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Q: dy If y = sin(6x – 4), then dx O a. 4 cos(6x – 4) O b. -4 cos(6x – 4) 6 cos(6x – 4) O d. -6сos(6x -…

A: y= sin(6x-4)

Q: 7T 2 Find 35 cos(7x) dx 5π 2 7T 2 35 35 cos(7x) dx = -5π လ

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Q: y = cev2z + Cze + C3 cos(v2x) + C4 sin(/2x) + Czev3z + Cge + c7 cos(/3x) + Cg sin(/3x)?

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Q: y" – 2y' – 8y = 3 cos 2x + 5 sin 2x

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Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: 1. [* sin' y cos' ydy 3

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Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

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Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

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Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

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Q: d2y/dx2 +4y=sin3x+cos2x

A: Given that:

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Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: Find and simplify the result whenever possible dx 1. y=x+sin2x 1. y = 4 1 sin' 5x 3 2. y sin5x - 3.…

A: Solving for the number 4:                                          4) y=3xcos(x3)-9 sin(x3)   To…

Q: 7T, 0 cos( {*) cos(2y)dx 2gin( gx) sin (2) dy 77

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Q: 4 cos 2y-3 dy 2у

A: NOTE: Refresh your page if you can't see any equations. .

Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x d'y dx? 1-cos4x 6. if y = 1+cos4x du

A: Topic:- derivatives

Q: dy Find , if Y = (1+ cosx)sinx dæ cos3x + cos³x – sin²x O cosx + cosx – sin³x cos2x + cos²x – sin?x…

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Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

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Q: ,In sec²(sin2y)dy can be evaluated by writing it as sec2y ! / sec²( sin2y) - 2 cos2ydy S. | sec2(…

A: To simplify the given integral.

Q: Find the value of zr» at the point (0, 3, 2) where a²y² + 2² – cos(ryz) = 10.

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Q: Find dy/dx in terms of x and y if cos² (4y) + sin“(4y) = y + 8. %3D

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Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,