16. y" + 4y' = 3 cos x + 5 sin x %3D a. y = C1+ C2e tx 23 ccs x 17 7 sin x 17 - 23 b. y = C1+ C2e*+ cos x + 17 -sin x 17 c.y = C1+ Czetr 23 cos x + 17 sin x 17 d. None of the above O A Ос O D

Q: 9 NO ION If g(x) = [ cos t dt, find g '(x). %3D x10 -sin (x) -10x cos (x) COS 1 cos (x°) %3 10x9 cos…

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Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: 14. Find the antiderivative of 5sinx In 5 cosx. a. 5cosx +3 c. 5sin x In b. 5sinx-2 d. 5 sin x + 7…

A: Anti derivative of the function

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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Q: y = In(cos 3x) %3D 1 (- sin 3x)(3) Cos 3x y' %3D y' = 1 (- sin 3x) cos 3x 1 y' = (3) sin 3x %3D -…

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Q: 3. If y = (sin 4x)², find y' %3D a.) 4 sin4x cos 4x b.) -4 sin4x cos 4x c.) -8 sin 4x cos 4x d.) 8…

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

Q: Sf(x) dx = 1 0.694 (sin(x) dx = 1 0.694 COS TX T C = 2 C 0.694 How? ==→ 1-C05 (0.69471) = 1694 -

A: To determine the value of C .

Q: %3D In( cosh(9x) + sinh(9x)) + In( cosh(9x)- sinh(9x)) = Select one: O None 0 9 O zero O9 cosh(9 x)…

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Q: 11 Evaluate (( sin(y²)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) b) 1-cos(x)) 1 - cos() 2 d) 1.…

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

A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts.…

Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O11x

A: Given: lncosh(11x-sinh(11x)) We know that   cosh(x)=ex+e-x2        sinh(x)=ex-e-x2   Then…

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

A: The detailed solution is as follows below:

Q: 1. y = In (3 – 4 cos x) + (4x – 5)5 2. y = x² tan x 3. y = x5 sin2x cos 4x %3D

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: 8 12. If y = then what is %? dx Vx+4' dy а. 4x(x + 4) dy С. dx = -4Vx + 8 %3D dx 3 dy b. dx -4(x +…

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Q: Find the most general antiderivative. 4 9 dx 4 sin-1 x - In Ixl +C 4 sin-1 x + 9 In |x| +C 3.…

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Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

A:

Q: 2. Evaluate the integral (cos (3r)sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

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Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

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Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

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

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Q: 1.Find dy/dx of the following: 5. y = Incose* tan x 6. y = ln(1-xe) 7. y=eta et 4. y= In x 8.…

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Q: 18. Evaluate fe³x cos 8x dx e3x a. [8sin 8x 3 cos 8x] + C 3x b. [8sin 8x + 3 cos 8x] + C 73 C. d.…

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Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

A:

Q: In( cosh(3x)+sinh(3x) )= Select one: O 3 sinh(3 x )+ 3 cosh(3 x) O- 3x 01 zero None O 3x

A: Formula to be used sinh x = [ex– e-x]2cosh x = [ex+ e-x]2

Q: he Solve the y)-Sy'(x)+8y(x)-4y(x)-xcos(x) equation y,0)-cos(x)+xsin(x)- 41 19 sin(x)+ cos(x)…

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Q: Solve for Linear DE of Order n: y′′−3y′+2y=cos(e^−x)

A: Using General Method of Linear D.E.

Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) e) y = (52)²x g) y =…

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Q: 1-Let :=x+iy then cosh(iz ) is equal to a-cos' y+ sinh' x b-cosh' y-sin'x e- sin' x+ sinh v d- None…

A: Let z=x+iy therefore, iz=ix+i2y=ix-y=-y+ix we know that  coshz=ez+e-z2 therefore, cosh…

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: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: • 8 If In = 7/2 e*cos" x dx, where n 2 2, prove that: %3D (a) In = 1-n[" /2 e-* sin x. cos"-1 x dx…

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Q: (2 - 3 sin 30 + y) dy- (9y cos 3p- p+1) do 0, y (0) = 2 Dy+4y-6y sin 3p+ q-20= 12 O y-y+9y cos 30- p…

A: We have to find

Q: L-' (In (s²+25)(s²+16) cos 5t-cos 4i O -2 cos 2t – 2 cos 31 O 2 cos 5t – 2 sin 4t sin 4t-cos 5i t…

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Q: 14. Find the antiderivative of 5sinx In 5 cos x .

A: Follow the procedure given below.

Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: 1. L(e** + e¬* + x²) S-4 s+1 s3 e3 2. L(sin 2x + e²x+3) : 2 + s2+4 s-2 Hint: e2x+3 = (e2x)(e³) %3D…

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Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O 11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O…

A: In this we have evaluate the equation ln(cosh(11x)-sinh(11x)).

Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: Show that an implicit solution of 2x sin?(y) dx - (x2 + 17) cos(y) dy = 0 is given by In(x? + 17) +…

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Q: 1) Find the indefinite integral S(3x* – 6vx + 3 cos x – 4e*)dx. 2) Find S 4(sin(6 sin x + x² + Vx))…

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Q: 4 sin 18x + 8 cos 9x dx. sin? 9x + 2 sin 9x + 5 Q10: Determine 4 А + C 9 In sin 9x + 2 sin 9x + 5| 4…

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Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

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Q: 8. Which of the following is the solution of * [2x + ycos(xy)]dx + xcos(xy)dy = 0 x? + cos(xy) =c x?…

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Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.