2. (Dª + 4D²) y = 48x + 96 sin 2x

Q: Find a result by using undetermined coefficients for ý + y = x² + x+sin(2x)

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Q: 2. Solve using any technique y" – 2y – 3y = sin r

A: First we find CF and then PI(by using the formula of PI of sin(ax)) and further find general…

Q: хах 3. S cos (2-3x2)

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

Q: 54 (b) y =. sin 2x. 4 Find

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Q: (D2 + 9)y = 30 sin 3x

A: The differential equation D2+9y=30sin3x, we have to find the solution of the given differential…

Q: - sin² ydy 6. 4 tan" y

A: As per the guidelines I can solve only first question

Q: b. y= 2 sin 2x+1

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Q: 11 3e²x + x sinx -47'+44= 3 e²x

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Q: (4D2 + 4D + 5)y = 40e−3x/2 sin 2x

A: Given that, 4D2+4D+5y=40e-3x2sin2x

Q: 3) (x²D² - 2xD+21)y=x³ sin

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Q: y" – 3y' - 4y = 3ez* у" - Зу'- 4у 2 sin x

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Q: y = 2 sin 2x

A: Given- y=2sin2x To Rewrite- The above function in the expansion form. Formula Used- sin2x=2sinx·cosx

Q: 15. (D* – 1)y : = sin 2x

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Q: Solve (D2+1)y=sin x sin 2x

A: Note that the particular solution can be obtained using the following forms: (i)…

Q: b) S (7x² – 5x² – 4)sin (3x) dx |

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Q: y= - 2 cos 4x +3

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Q: dy Solve cos2x ty3D tanx

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Q: 4)y = 2 sin (3x +) - 1

A: Given: y=2sin3x+π5-1

Q: Solve: (D² +1) y = x² sin 2x

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Q: Solve y' + 2 sin(2x)y = 2 sin(2x), y(π/2) = 3.

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Q: 2r sin 1 (r²) d»

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Q: y"' + y = 2 sin 4x + 4e¬5x %3D

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Q: 8) y'+y=17 sin(2t), y(0) =-1.

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Q: 2 sin (3x) d%

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Q: 7- y" + ²y = cos 2t, ²4; y(0) = 1, y'(0) = 0

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Q: SOLVE FOR X y = 1 + sin (7)

A: Solve equation for x

Q: solve y′′+ 9y = sin^2(3t)

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Q: Solve (D² - 2D + 5) y = sin (2x) + 17x cos (2x) — 15x -

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Q: Sketch : 3 sin (x-T/4) +2

A: Start with the standard trigonometric function y = sin(x) and transform it to get the graph…

Q: 26. y" – 6y' + 13y = xe3* sin 2x |

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Q: che general solution of -V - 6y = 6x3 + 26 sin 2x

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Q: What is the midline equation of y = -4 sin (2x-7)+3?

A: Given y=- 4 sin (2x-7)+3

Q: 2. y = ₁³x cos x + c₂e³ 3x Ge 3x sinx

A: Find out the differential equation by elimination of arbitrary constants.

Q: y" – 4y = sin(5x)

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Q: The equation (tan²x+3y²)sec²xdx + (3tan²x + y²)dy=0 can be solved by

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Q: 4) y" +4y=16x sin2x

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Q: 2) y = sin(3x²ex)

A: Find the derivative

Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…

Q: Solve: y" + 9y = 9csc3x O y = C1 cos3x + C2 sin3x – 3xcos3x + sin3xln(sin3x)

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Q: 1. D² {Sin ² x 3 2. JD²-15² √2e²x3

A: Here D is the differential operator. D=d/dx

Q: S(sin2z – 3cos2z)°dz

A: Here, (sin 2z-3cos 2z)2 =sin22z-6sin 2zcos 2z+9cos22z=sin22z+cos22z-3(2sin 2zcos 2z)+8cos22z=1-3sin…

Q: 2. Solve the DE: 2y' - y= 4 sin( 3x)

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Q: Evaluate the integrals

A: Given integral, ∫π23π41-sin2x dx

Q: Solve (sin23x)dy= dx cot3x + C 3 cot3x O b. y= 3 sec3x O C. y = O d. y = sec3x + C 3

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Q: 2. Sin 2x dp X UIS 6.

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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: 1 sin(2x)= sin(2x) -125 (D²-1)

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Q: 1. y' + 2 sin 2TTX

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…