s+2 is equal to s+4 A (cos2t+ sin2t) cos2t + sin2t e-2tcos2t D cosh2t + sinh2t B

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Q: 3 S² x³ cos x ²dx 6.

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A: To evaluate the integral ∫x dxcos2-3x2.

Q: 8 +10x-32+x? cos 2x 4 Find : (a) y = %3D x2

A: Given y we have to find dy/dx as shown below

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A: We have to find the solutions of - 2sin2(x)+3sin(x)+1=0    between [0,2π) We will solve the given…

Q: 8. (a) 2e' (cos 3t – 3 sin 3t) (b) 3e-2 (sinh 2t – 2 cosh 2t)

A: Given functions: (a) 2etcos3t-3sin3t (b) 3e-2tsinh2t-2cosh2t   We know that,…

Q: (b) D₂f = 2 cos(xy + 2z) Dzzf = -4 sin(xy + 2z) Dzzyf = -4x cos(xy + 2z)

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Q: Solve the equation v2 sin x - 2 cos x=-1 for – 7SxST.

A: This question is based on Trignometric application.

Q: find general Solution (D²+6D. Sin 4X to

A: Given differential equation is : D2+6D+16y=sin4x To find the general solution.

Q: Solve 2 cos (z) – 5 cos(1) + 3 = 0 for all solutions. where ke Z

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Q: If f (x) = cos? (3r – 5) then f' (x) = 6 cos (3z – 5) 3sin? (3r – 5) -2 sin (3r – 5) cos (3x – 5) D…

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Q: The solution of sin'x + 2sinx - 3 = 0 on 0°Sx< 180° is:

A: ⇒sin2x+2sinx-3=0⇒sin2x+3sinx-sinx-3=0⇒sinx(sinx+3)-1(sinx+3)=0⇒(sinx-1)(sinx+3)=0⇒sinx-1=0  OR…

Q: -3x cos 2x da A) - cos 2x - 3x sin 2x + C B) - 2x- sin 2x +C s 2x - sin 3x + C D) - cos 2x - sin 2x…

A: Since you have posted multiple questions . As per the guidelines we will solve the first question…

Q: Solve using the Method of Coefficients: y'' + 3y' + 2y = 7 cos x - sin x

A: The given differential equation

Q: Evaluate D(sinx – 4e2) D³(sinx cos x-32 e В -cos x-32e2 C) -sin x-32 e2x (D sin x-32 ex A

A: The objective is to evaluate, D3sinx-4e2x

Q: a. Solve 2 cos(2x) = √2 for x

A:

Q: Q(3) Solve (D3 + D²)y = 3x2 + 6 sin x – 2 cos x

A: As per our guideline,we are supposed to answer only one question.Kindly repost the other question.…

Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: Solve for x: 3sin x + /2 cos x: V39 0 < x < 27.

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Q: Q5: Find: a) £[3-5e²t + 4 sin t - 7 cos 3t] b) C- 3.s s²+16 5 s² +

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Q: sin(8t) -2t O a. r(t) = e cos(8t) +e2t O b. x(t) = e 4t cos(8t) – e t sin(8t) COS O c.(t) = e2t…

A: Given,         dxdt=12x-8y        dydt=16x-4y

Q: Find the General and Particular solution of = -8 sin 4x ; y = 6 when x = o dx

A: As there are multiple questions, first one is solved here.

Q: Find the general solution to y" - y' = 5ex - sin 2x

A: Given differential equation, y''-y'=5ex-sin2x

Q: Solve the general solution y'=cos2x cosy

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Q: Evaluate D³(sinx - 4e²x) A -sin x-32e²x B -cos x-32e²x (C) с cos x-32e²x D sin x-32e²x

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Q: Find -2s3 + 9s² – 8s + 18 -1 s (s2 + 4) (s + 1) (3-5e+3 sin 2t ) (4 - 5e' + 2 sin 3t) (1-3e+3 sin…

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Q: Find a particular solution to y" +4y = - 12 sin(2t).

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Q: Q: Solve y+8= Cos (x) ナ3sin(2x)

A: Given: y''+y=cos x+3 sin 2xCE: m2+1=0⇒m=±iCF: e(0)x( Acos x +B sin x)=Acos x +B sin x

Q: Find the general solution of cosec"x2= cos²y(separate variable) %3!

A: As per our guideline we are supposed to answer only one question.kindly repost other question. The…

Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: Solve the equation: 2cos2 x + cos x - 1 = 0, 0 ≤ x &lt; 2π.

A: The given equation is 2cos2x+cosx-1=0. Solve the above equation as follows.

Q: General Solutions (D2+2D+2)y=5cosx+10 sin2x

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Q: Find the general solution: 2y" + 3y' +y = 2e2 + x² + 3 sin(x).

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Q: Solve the equation on the interval 0 s 0 < 2r. 2 sin 0 = sin 0 %3D 5T 0,6 22 3 3

A: use trigonometric table to find the angle.

Q: Σ Σ cos C. n = 1 2n2 – 1 |

A: The objective is to find the sum of the series.

Q: Solve the equation sin 2u = 1, for 0 … u 6 2p.

A: To solve the equation for 0≤u≤2π, sin2u=1

Q: Solve (D2+9)y=cos 3x+sin2x

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Q: A particular solution of y" - 3y' – 4y = 2sinx 5 -cosx 17 a. 3 COSX - 17 5 sinx 17 b. 3 -sinx 17 C.…

A: find roots for the homogeneous system

Q: The solution of Sinx dx - x sinx+ y cosx= 0 is (y– 1) sinx =? A C-x sinx B C+ x cosx с-х cosx D C+ x…

A: sinxdydx-xsinx+ycosx=0sinxdydx+ycosx=xsinxddx(ysinx)=xsinx

Q: What is r = -12 2 cos 0-7 sin e 2y - 7x = -12 in Cartesian form? x² + y² = -12 2x-7y

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Q: Evaluate D³(sinx - 4e²x) (A) sin x-32e²x (B) -cos x-32e²x C -sin x-32e²x D cos x-32e²x

A: Finding the third derivative of the function

Q: T/3 2 +3 sin(x) dx cos² (x) Cos?

A: Topic:-  definite integration

Q: Solve 2 sin(2w) +3 cos(w) = 0 for all solutions 0 < w < 2T W =

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Q: Find the solution of the equation if0 < x<÷n T. 4sin³x – 3 sin x = 0 -

A: We know that, sin3x=3sinx-4sin3x. Also, sinx=siny⇒x=nπ+-1ny n=0, ±1, ±2,...

Q: Evaluate D6(cosx+e-2*) (A sin x +64e -2 B cos x – 32e-2r (c - sin x – 32e-2x cos x + 64e -2x |

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Q: Solve : = - 3 y t16y =0 fus uwer. = 3 cos 4x- Sin

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Q: (D3- D2)y = cos2t a. y, = -cos2t +sin2t 10 20 b. y, = - cos2t -sin2t 10 20 c. p =cos2t- sin2t 10 20…

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Q: Find LT of (i) e-*(2 cos 5t – 3 sin 5t) (ii) e²ª cos² t (iii) e“ sin 2t cos t ,4t

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Q: 2. Is it possible to write sin (37x) as a linear combination of sin(2rx) and sin(Tx) for all values…

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Q: (2D – 5)y = sin 2x – 7 cos 2x -

A: