(10) The result of (D-3D D, +2D;)sin(x-2y) is

Q: (D² – 5D + 6)y = 15 sin x – 15 cos x - -

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Q: 4 b. [√x ln xdx, 1 4 ㅠ C. fx√4-xdx, d. fx sin (2x) dx. 0

A: Solve the following

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

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Q: If fx*cos x dx = f(x) - j2xsinx dx, then f(x) is A. 2 sin x + 2x cos x+C B. xsin x +C %3! C. 2x cos…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2) find the radius and coordinate center for the equation 2x42y+10y-12х-20-0 3) prove that sin 2x…

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Q: y" +3y' – 2y = e-2*[(20x + 4) cos 3.x + (-32.x + 26) sin 3.x] |

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Q: Q4A/ If y=x sinx+√1-x², then dy/dx is: 1.√1-x² sin-¹ x 2. sin(x) O 1 O 2 x cos(x) sin(x) sin(x)2

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Q: a. f(x) = V3x3 – 2 %3D b. y = (Vx + 1)(x² – x) 2x5-3 c. f(x) cos x d. y = sin(4x²)

A: All the questions are solved below.

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: 3.4.4 Evaluate ff sin(x + y) dx dy over the triangle whose vertices are (0, 0), (2, 1), (1, 2).

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Q: (x-2) (g-9) 2- 3X+uX- %3D 29-u | Sind general Salantion

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Q: using undetermined coefficients (D^2-2D+2)y=24e^x sin3x

A: Given: (D2  -2D+2)y=24ex sin3x

Q: y(x) =- 10 n +2x' +8x' + 48) +qe* +c, sin(x)+ c, cos(x)

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Q: 1. f(t) = -2e-14t + 5 Cosh(4t) 2. f(x) = 4 Sin(7x) + 480

A: We will use Laplace transform of some standard function to solve this.

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: 3) = + sin (4) r = y(In y- In r+1)

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Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

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Q: F(r) = 5x sin(/2x) – 3 cos(/2x) +xe³r sin(3x) + 2x ?

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

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Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

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Q: | (6e"+6x° +4 cos x + 2)dx = %3D 6e + x° + 4 cos x + 2x + c O e – x° + cos x + 2 + c 6 O e + x° 4…

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Q: cos x 3. f sin³x dx (2 + sin?x) + C 3 4. S* x sin 2x dx 1-9x2 5. S sin-1 3x dx + x sin-1 3x + C 3

A: Q - 3

Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

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Q: 5. 2 sin7 0 cos Od0 )dy 1 6. JF(ylny 9-y².

A: Use the method of substitution to solve a given problem.

Q: 1. / 2dx 3D 0 + С %3D С 2. Sx²dx = 2x + C %3D 3. S 5x*dx = x5 1 4. Sdx = + С 2(х2-5) x2-5 5. ſ tan x…

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Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

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Q: |-3y{(x)+4y,(x)- y (x)+ 2y,(x)+6x– 3– 4sin(x) = 0 2 y (x)- 3y,(x)– y,(x)– 4x+2+3 sin(x) = 0 %3D

A: Given -3y1'x+4y2'x-y1x+2y2x+6x-3-4sinx=02y1'x-3y2'x-y2x-4x+2+3sinx=0

Q: - 6 3 y =x sin x + x cos 2

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Q: The general solution of (D²-2D+1)y=2sin x y=C1eX + C>XeX + sinx By=c₁еx+c₂xe* +2sinx Cy=c₁еx+c₂xe* +…

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Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

Q: 8. (D² + 100)y = -300 %3D a. y = C, cos 10x + C2x sin 10x - 3 %3D b. y = C1 cos 10x + C2 sin 10x- 3…

A: Solution: (D2 +100)y =-300 The Auxiliary equation is m2+100 =0 m2 = -100 m= 10i , -10i

Q: The general solution of (D2-2D+ 1)y=2sin x A у-сје*+ с2хе* + sinx + cos х y=cqe*+c2xe* +2sinx В ©…

A: Note -  Acc. to Bartleby guidelines we are supposed to do only one question. If you want more to be…

Q: B sin 5x+ sin 3x 1 sin 5x+-sin 3x+c 6 I 10 fcos 4x cos.x dx = ?

A: Given :∫cosxcos4xdx

Q: 35) y = -4 sin x 4+ 2+ 2n -2+ -4-

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Q: 0<x<T (-1)"-1 f(x) = { 27-x COS nX n<x< 27

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Q: Find the general solution of: y"-3y 8e* + sin 2-

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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: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i 5 .5 и 3

A: The function is given by  fx, y = sin8x-5y The point is x, y = 5, 8 The unit vector is  u = 35i-45j…

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: 3. Find the general solution of (2y cos x + sin*x)dx = sin x dy a. y = sin²x(- cos x + C) c. y =…

A: follow next step

Q: [²(x². x7-4x⁹+ (A) True B) False sin(x) (1+x²)² dx=0

A: The given integral is ∫-11x7-4x9+sinx1+x22dx. We have to evaluate the given integral.

Q: Q-4) Find the general solution of the Cauchy-Euler equation x'y"+ xy'+4y = sin(In x)

A: Solve the Cauchy Euler differential equation

Q: 2. [ (1–3x)sin(}x)dx 4w dw 3. [* w°e™ dw w²e* -1

A: This question is taken from the definite integral in which we have to find the integral of the given…

Q: T/2 | cos(x)/1+sin(x)dx = 6. A. 2/2-1 (2V2 -1) 2V2 +1) В. С. D. 3 (1-7*) Е.

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Q: 11) у%3D V1- sin 2.x y =

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Q: y" – 2y' + y = [-6x – 8] cos(2.x) + [8x – 11]sin(() 2x) %3D

A: We have to solve the differential equation y''-2y'+y=[-6x-8]cos2x+[8x-11]sin2x.

Q: 3 The value of (Isi n(x)| + x²) dx is .a 2 f(- sin(x) + x²) dx 0 .b .C 2 f(sin(x) + x²) dx -3 .d 3 ,…

A: Let's find.

Q: .4. (c) y = x*; y = sin(Tx/2); about x = -1

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Q: 3. у" — у' — 2у %3D5 sin x y(0) = 1, y'(0) = -1 -

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