For a Cauchy-Euler DE the roots of auxiliary are m = -3 ± 3i then Ye = x (c, cos(3 In x)+ c2 sin(3 In x)) Ye = e -3* (C, cos(3x) + c2 sin(3x)) Ye = x(c, cos(3x) + c2 sin(3x)) -3x Ye = c1 e-3* + c2x e None of These.

Q: 3. The integral of sin24x cos4x dx is a. (1/4) sin³ 4x + C b. (1/3) sin³ 4x +C c. (1/12) sin³ 4x+ C…

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A: Solution of the differential equation

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Q: 19. f(8) = 8 - sin²(20) 9 8sin(20)cos(20) a. f'(0) = 9 32sin (20)cos(20) b. f'(8) = 9 32cos(20) c.…

A: fθ=89sin22θ take derivative f'θ=ddθ89sin22θ

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A: In this question we have to solve the given differential equation.

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Q: If f(x,y,z)=In(x²y+sin² 12

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Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

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Q: The integral of the given function | sin 9x cos 4x dx is equal. .... 13 cos(5x) — 5 сos(13x) А. + C…

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Q: If 1, = |x" sin8x dx , Then 64 I,+n(n-1) I,-2 Select one: O- 8x" cos8x +n x" 7 sin8x O + 8x" cos8x…

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Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

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Q: Evaluate J J-36z² dz 1 sin (5æ) + C 6. O_ 1 -1 sin (6x) + C O_1 sin (5x) + C 6 -1 1 Osin1 (6x) +C 6.

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Q: 5) Evaluate the real integral 27T 1 de (5+ 3 cos 0)(13+5 cos 0) by complex variable methods, i.e.,…

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Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

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Q: 17. (D+ + 2Dz + 1)y = 5– 3x2 a. y = (C, + Czx) cos x + (C3 + C4) sin x – 3x2 + 17 b.y = (C1 + Czx)…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: 1 Evaluate | (x²sin y- xcos(y))dy O 2sin y-3cosy + C 6 -3sin y+2cosy +C 6 x2(1- cos(1)) – xsin(1) +…

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Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

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Q: H.co/ prove That;. dz 1-2 Cosh2=

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Q: (d) Show that there is some x with 0 < x < 2 such that x2 + cos(ax) = 4. %3D

A: Solution-