(2D – 5)y = sin 2x – 7 cos 2x -

Q: y" + 3y' +2y=(− 4x² − x + 1)cos 2x − (2x² + 2x +1)sin 2x

A: To solve the differential equation of the form y''+ay'+by=A(x)cosbx+B(x)sinbx Assume the particular…

Q: 3. S sin®2y · /cos2y d|

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

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Q: 211 211 cos nx dx= [cos %3D %3D nx cos nx dx =0.

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Q: 6. y" + 3y'-2y e-2* [(4+20.x) cos 3x+ (26-32x) sin 3x]

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Q: 1. (xy' – y) cos ( 2у COS -3x4

A: Since you have asked multiple questions, we will answer the first question. If you need answer for…

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

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Q: +3x2 B) Find dy/dx if : (****")) (v)² = sin (cos³

A: Differentiation chain rule

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: Scos2x (2 2 Cos 2X (2 cos 2X -1) dx

A: Given integral is ∫cos 2x2 cos22x-1dx To find: Value of the given integral. Formula used: 1) cos…

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

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Q: Find: O d: x-6,X-1 dy 3 23=Sin (cos 8x)

A: 1 .y=45x3-6x2+x2-12. y=sin(cos(8x))

Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

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Q: y" + 4y = 4 sin(2.x) + 8 cos(2x), y(0) = 0, y'(0) = 1.

A: We have to find solution of given differential equation. We will first find Complementary solution…

Q: / – 9x* sin²(7y") = 9x* cos²(7y/") What is y(4) if y(0) = 8? %3D %3D

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Q: y" + 4y = 4 sin(2x)+ 8 cos(2x), y(0) = 0, y' (0) = 1.

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Q: 8) y" - 2y'+ 2y = 2e" cos(x)

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Q: (6e + 6x°+ 4 cos a + 2)dx 6e + x° + c 4 cos a + 2x +

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: y³x2 + yx³ - 20y² – 10y = 0 sin(x?) = cos(y³)

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Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

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Q: 1(y) = In(sin(cos(y²))) %3D

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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: 3e" + 3x + 10 cos x + 2)dx .2

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Q: y" – 2y' – 8y = 3 cos 2x + 5 sin 2x

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Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: 2 X 1 t3 COS 4- x² dx 2 -2

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Q: -9 4s4+s*V5-6 ds s4 1-cos? x dx sin x 2. 3.

A:

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

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Q: dx+ 1.5 +§ (5r – 15)cos (5х — 15)сos dx COS 1.5 Jo (5x)cos 1.5

A: We have to apply the integral by parts.

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: 5. (D² + 16)y = 24 cos 4x – 32 sin 4x

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Q: 3. 2 +X-1 dy 2=Sin (cos 8x) %3D

A: 1) Given that y=4x35-6x2+x2-1 y=4x35-5x2-1 we have to find the derivative of 'y' with respect to 'x'…

Q: d²y 9. +y= sin 3x cos 2x 2

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Q: y = sin(3x) + cos(0.5x)

A: Given: y=sin(3*x)+cos(0.5*x) We have to determine the value of y,where x varies from 0 to 2pi in an…

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

A: Topic:- solution of differential equations

Q: æ' = y – 5 sin (3t); y/ = -4x + 17 cos (3t) , ift = n, x = 7; y = -4

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Q: x7+3x2. Find dy/dx if: (y)² = sin (cos³(* +3: *)) %3D 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: Integrate x cos(2x^2+7) dx. Select the correct response: O sin (2x^2+ 7) + C

A: Integrate using substitution method.

Q: 1 S (4x4 – e3* + cos(2x) – + 5* ) dx - x-1

A: First you need to go through the formula of calculus. Specially go through the details of the…

Q: Hf sin x = A + B cos 2x +C cos 4x, then A = %3D C =

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Q: 11. y= e4x %3D 2x 12. y= e cos 3x

A: We can solve this question using chain rule and product rule of derivative.

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

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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: Find 2: (a) y = cos(1 1x + 5x)

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Q: 5. S sin(3x)dx (a) 3cos(3x)+ C (b) †cos(3x)+ C (c) – 3cos(3x)+ C

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Q: 7. Find (a) y = (x* + 5x) cos 5x %3D dx

A: We can find the derivative using product rule as below

Q: (3e + 10 cos(x)) dx ntegral =

A: Integration problem....