/2a cose 2 Se sin æd &d pdp 0 0 0

Q: cos2x dx 1 sin 2x- 16 12

A: The objective is to find  the integration.

Q: x=-2+4 cos 0 and y=1+5 sin 0

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Q: y" + 4y = 16t sin 2t

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Q: 54 (b) y =. sin 2x. 4 Find

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Q: -Tt/2 S 3 sin 0 + 5 cos0 d0 -t/2

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Q: 1. (D² + 30+2)y=24 cos 3x

A: First we find complementary function then particular integral and then general solution as in next…

Q: 2e cos 2t

A: Given,       2elncos2t

Q: 1. f(t) = -e-3t sin 4t + 3

A: L { sinat } = as2+ a2 , L { eat f (t) } = F ( s- a) where  F (s)  is Laplace transformation of f(t)L…

Q: 8. y = (cos 3x)V

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Q: b. y= 2 sin 2x+1

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Q: 2m 14. sin x dx

A: Topic- trigonometry  note- As per our guidelines i have to do only one question other can be…

Q: 9) |x² cos(5x? )dx

A:

Q: - 4cos3 0 sin 0

A: To find the value of  -4cos30sin0

Q: 15. (D* – 1)y : = sin 2x

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Q: 7 sin(2t) + 4 cos(t) = 0 %3D

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Q: V3 11. cos(3x) = %3D

A: cosθ   is negative in 2nd and 3rd quadrant

Q: L[(sin2t+cos2t)² + et sinh(10t)]

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Q: Solve (D2+1)y = sin x sin 2x %3D

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Q: 1- cosx dx A -2/2cos- +C B 2/2cos- +c -2/2 sin-+C 2 D 2/2 sin- +C

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Q: Find integral.

A: Consider the indefinite integral ∫-6x cos 5x dx Use the integration by parts to solve the indefinite…

Q: y = 2e cosx

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Q: Find fe2" sin(2x)dx

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Q: 144 142 cos (4x*) dx dy 0 „1/2

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Q: Evaluate the integrals

A: 71). To evaluate the integral: ∫tan2x+sec2xdx Solution: We know that, sec2θ-tan2θ=1⇒tan2θ=sec2θ-1…

Q: y у +4у%3D 16t cos 2t

A: We have to solve the differential equation…

Q: 3. x = cos³ 0, y = sin 0 4

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Q: y"' + y = 2 sin 4x + 4e¬5x %3D

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Q: 1 cose sin 0 2/3 2 csce: 3

A: Explanation and solutions is given below....

Q: 3. S sin³ 0 cos³ 0 d0

A: Given

Q: cos° (2t) 23. sin (2t) dt

A: Use the formula sin2x+cos2x =1.

Q: のSX 3 +23 +5y +5y = e + 40 Cos loX-190 Sin lox

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Q: y" – 4y = sin(5x)

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Q: •TT/6 4. S sinx sin2x sin3x dx

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Q: Solve xdx - x² (cot 2y + x2y cos 2y)dy = 0

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Q: S sin(ax)cos(ax)/3 – cos(2ax) dx

A: Sin(2ax) = 2*Sin(ax)*Cos(ax)

Q: 11. y = (x + y) 12. y =x sin -1x + 1 – x2

A: Let's find.

Q: - Solve y"+y = cos(x) +3 sin(2x) %3D

A: Given- y''+y=cosx+3sin2x To Find- The value of the above differrential equation.

Q: 1/2 cos²(æ) sin°(x) dx COS 0.

A:

Q: T/4 sin2 x 2. :- cos? dx CoS2 COS x 7/4

A: To find the value of the given integral.

Q: ++++4y= 10 Sin 3X

A: Note: As per our company guidelines we are supposed to answer only first question. (11) The question…

Q: 10. 4 COS dx 2

A: the given integral is: ∫cos4x2dx we have to evaluate the given integral.

Q: T 4 0 sin3 xdx

A:

Q: 1. S 3 cos("/x) x2

A: "Since you have asked multiple questions , we will solved the multiple questions for you. If you…

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

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Q: 1. y" + 4y = 4 cos x + 3 sin x – 8 %3D -

A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 12) y = 3 cos 0 3 T/2 -T/2 Зп /2 21 5T /2 3T 71/2 9T /2 -TT TT -1 -2 -3 2.

A: We have the function y=3cos12θ

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: y" + 8(sin* πx)y =0, 0<x<1and y(0) ν(1) 1 =

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Q: 5TT i sin' cos*dx 4x. 4x, 8. 5

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Q: 2. 6 cos 2x dx

A: To evaluate the given integral.