19. y = -3 cos 2x 20. y = 5 sin 2 AAMA A

Q: 3. S sin®2y · /cos2y d|

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Q: 3. Solve: cos xdx + ( 1+ | sin ædy = 0 %3D

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Q: 1- Calculate the value of y if: a-y= sin "(0.25) + sinh (2). b- y= sinh (15)+cosh"(31)

A: Note: According to our guideline, we will answer one question. As the exact one is not specified.…

Q: 1- Differentiate. a- Y= 2 e2+1 b- Y= -2 sin?x c- Y= 3sin2x - cos 4x d- tanv(1-x)

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Q: s sin(3x) + cos(5x) – sin sin)ax |dx

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Q: S .2 4. sin x cosx dx

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Q: 1. S sin’y (2 – 3 cos y)°dy

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Q: S 5 sin(3x)e2cos(3r)dx

A: Solve integral by substitution method:-

Q: 13 9 2 cos dx dy dz =| 0 0 3y (Туре an exact answer.)

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Q: 1. (3tanx 2 cos y) secx dx + tanx siny dy =

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Q: 211 211 4- Cos nx sin nx dx sin 2nxdr 0.

A: The detailed solution is as follows below:

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

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Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: x4 1 If u = tan(- + y° x² – y² - then show that ди du + Y- ду X - = sin2u dx

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Q: y = Ceax cos(bx) + C2eax sin(bx); a and b are parameters y = Ce2x cos(3x) + Cze2* sin(3x)

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Q: 25. y = 2 cos yA 2 28. y = 2 sin ) -2TT -2 31. y = 3 sin (2x) (A)

A: In this, the amplitude is multiplied by 2 and x is scaled by 1/2.

Q: 1(y) = In(sin(cos(y²))) %3D

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

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Q: Evaluate the integrals

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4x /² sin () cos (+) sin (²) dx (Consider initially the first 2 terms) 3

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Q: e csc 20 In (ecos 2 ) Ince cos CoS 20 28) Sin2 20 OP

A: Given integral is ∫ecsc2θlnecos2θsin22θdθ since lnex=x, so lnecos2θ=cos2θ The integral becomes…

Q: 1/2 sin 12 y cos' y dy y

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Q: 3. 2 +X-1 dy 2=Sin (cos 8x) %3D

A: 1) Given that y=4x35-6x2+x2-1 y=4x35-5x2-1 we have to find the derivative of 'y' with respect to 'x'…

Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

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Q: 9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

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Q: LE (4y°x² + Sin 2x + Cos²3y) dy dx

A: we have I = ∫-11∫-2-1(4y3x2 + Sin 2x + Cos23y)dy dxlets slove each term separatelyI1 =∫-11∫-2-14y3x2…

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: .3 4 cos³ 4y /sin 4y dy

A: To find out the integration.

Q: 2. Eliminate all the arbitrary constants in the equation as follows: y = Ae2x – e-5* (B cos 2x + C…

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Q: 21) (1 + cos 9t) 2 sin 9t dt

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Q: æ' = y – 5 sin (3t); y/ = -4x + 17 cos (3t) , ift = n, x = 7; y = -4

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

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Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

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Q: 2) x³y? = 2x + 2y3 3) y = sin?(x) – cos³(2x) + 2 www. .

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Q: 1- Calculate the value of y if: a- y= sin (0.25) + sinh (2). b- y= sinh (15)+cosh (31)

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: у" + 4y' + Зу %3D sin (e*)

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Q: 7. y" + y = 3 sin(2r) +t cos(2t)

A: The general solution of an ordinary differential equation of the form;…

Q: S 4 cos (x) sin (x) dx = %3D

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Q: 4. S(1 – cos 4u) du 5. S sin x cos x dx

A: 4) Given:        ∫1-cos4udu Apply linearity:    =∫1 du-∫cos4u du     =u-∫cos4u du

Q: 1- LS7 cos(y)esin(y)+9x dydx 2

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Q: y = cos 3x a. 3 sin 3x b. - sin 3x c. sin 3x d. -3 sin 3x с.

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Q: @2) find to dx 2. y=CoS 2' Sin e

A: To find the dy/dx of the given function

Q: (a) y" + 3y' – 2y = -e2" (5 cos 2r + 9 sin 2a)

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Q: 1. If x-y? = 25, then y" = %3D a.) b.) c.) - d.) - 2. If y = cos(3x+1), find y' a.) 3 sin(3x+1) b.)…

A: Given:   (1) x2 - y2 = 25    (2) y = cos(3x+1)

Q: 7/2 d sin dx dx COS

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Q: 13. y = -3 sin 2mx 15. y = -sin ix 14. y = -2 sin mx 16. y = -sin jx

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Q: 9) S 2 cot 2x cos x dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1- Calculate the value of y if: a- y= sin (0.25) + sinh (2). b- y= sinh'(15)+cosh (31)

A: according to the guidelines of bartleby I will do only first question please ask rest of the…

Q: 7+2 sin y -dy = D cos ?y

A: on solving this we get the