-) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of undtermined coefficients.

Q: Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y" +…

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Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

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Q: x = y + 3x¹ sin² (2) to separable equation then solve it. 1. Reduce the DE. x

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Q: 3. Simplify x(t) = 3 cos(27200t + + sin(27200t + to the form x(t) = a cos(27200t + 0) where a and 0…

A: To convert an expression of the form Acosx ±Bsinxmultiply and divide by A2+B2=A2+B2AcosxA2+B2…

Q: 1. If x'y" + xy' + (x². 4 - -y=0 Y=x sinx , and y= y,v. Which of the following x>0 equations…

A: Solution:    Given:                  x2 y"+ xy' +(x2 14) y =0, x.o                 y1 = x-12…

Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

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Q: What will be the neutralizing factor of 7sin(4x +sin(2x)dx when it is first evaluated using product…

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Q: 7. y - 5y + 7y" - 5y' + 6y = x² + 3x - 5 Ans: y = C₁e³x + C₂e²x + C3 cos x + C₁ sin x + x² + ²x -…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Solve: (cos x) · (dy/dx) + y sin x = 2x cos2 x, y(Tt/4) = (-15/2-n2)/32.

A: The given differential equation can be written as :            dydx +ytanx = 2xcosx So, the…

Q: If z = x2 + y² and x t cos 2r and y = r sint, then %3D a2z is at2 (A) 2 cos²(2r) + 2r? cos?(t) – 2ry…

A: Given  z=x2+y2      and x= t cos 2r ,y= r sin t First substitute x,y values in z  Then derivative…

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

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Q: on of y" – 2y' + 2y =

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Q: π/2 1-z [²6² x cos ydzdydx = = [Show your solution.]

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Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA.…

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Q: Which of the following equations can be solved using the method of undetermined coefficients? O y" +…

A: The solution are next step

Q: Find the solution(s) of the equation sin (x + 1) = v2 cos e within the interval 0 < x < 27.

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Q: 2хy? + 4 %3D 2(3 — х2)у' ) dy

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Q: Determine the form to be used for x when using the method of undetermined coefficients. x" + 2x = 8…

A: Given DE is  x"+2x=8sin(2t) ......(1)

Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

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Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

Q: 2. verify that each of the following equations has the indicated solution : • y" +4y =0 y=ae2x+bxe2x

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems. First problem:…

Q: What is the particular solution of (Dª + 4D² – 1)y = 44sin3x O a. cos3x O b. cos2x O c. sin3x O d.…

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Q: 1) Solve for r, 0 <x< 2n. sin (4x) – sin (2x) = 0

A: Given that: sin(4x)-sin(2x)=0              and             0≤x≤2π

Q: y" + 4y = -12 cos 2x - 4 sin 2

A: I am attaching image so that you understand each and every step.

Q: Find the solution. dy sin x x-+2y +2y = y (2) = 1 dx (A) y = (4 + sin 2 + cosx?) /x2 B в су %3D (3 —…

A: Given differential equation  xdydx+2y=sin xx,   y2=1 Linear differential equation with initial…

Q: y′′ + 16y = 32 cos(4x) − 24 sin(4x)

A: The given differential equation is        y'' + 16y = 32cos(4x) − 24sin(4x)…

Q: Question 2 Find the solution to the DE. (y-x+xycotx) dx + xdy=0 xysinx=C+ sinx - xcosx Oy=(c +…

A: Concept: For a differential equation of the form P(x,y)dx+Q(x,y)dy=0 The differential equation is…

Q: Solve on the interval [0,2n). (2 cos x + V2) (2 sin x – 1) = 0

A: Some trigonometry angles: 1.)sin90°+θ=cosθ2.)cos(90°+θ)=-sinθ

Q: Find the solution. dy X-+ 2y = dx sin x y(2) = 1 A cy = (3 – cos 2x – tanx)/x? B x = (2 + cor2 –…

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Q: Applying the method of undetermined coefficients, solve y" + y' + 8y = (10x² + 21x +9)sin 3.x + x…

A: Given differential equation, y''+y'+8y=10x2+21x+9sin3x+xcos3x To find the auxillary equation,…