Find the general solution of the linear differential equations. (D* – 4D² ]y= 36 9x3 a. y = C, + C2x + Cze2x + C4xe2x – * 2 b. y = C, + C2x + C3e2x + C4xe²x + 9x 2 c. y = C, + C2x + C3e°2x + C4xe¬2x _ x* d. y = C, + C2x + C3e2x + C4e¬2x – * 9x e. none of these

Q: 10. What is the general solution of the nonhomogeneous differential equation (D² – D– 2)y = 6x +…

A: Given differential equation is D2 -D-2 y = 6x +6e-x  This is non homogeneous differential equation.…

Q: What is the differential equation of the solution: y = C1e-6x + C2e4x ? a. y'' - 2y' - 24y = 0 b.…

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Q: Find the general solution of the following differential equations: 1. D2 − 6D + 9)y = 0

A: We'll answer the first question, since the exact one wasn't specified. Please re-submit a new…

Q: Solve the second order differential equation ÿ + 2y = 3 cos 2x A:y = c, cos(vZx)+c2 sin(vZx)+…

A: General solution to a nonhomogeneous linear differential equation a2(x)y''+a1(x)y'+a0(x)y=r(x) is…

Q: Determine the solution of the differential equation 2y(4) + 3y" + 2y" + 6y' – 4y = 0 %3D y = C,e2x +…

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Q: the general solution to the second order linear differential equationd^2y/ dx^2 − 14dy/ dx + 51y =…

A: We will find the solution.

Q: Solution of the Cauchy Differential Equations x²y=2xy=6y = 0 is.

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Q: Find the solution of the differential equation у" — 16у 3D 2е\x y = C,eªx C2e¬4x + +xe4x а. 4 b. y =…

A: The given differential equation is y''-16y=2e4x .............................. (1)  for the…

Q: Determine the solution of the differential equation 2y(4) + 3y"" + 2y" + 6y' – 4y = 0 X а. y = Ce2x…

A: A detailed solution is given below

Q: Find the general solution of the linear differential equations. (D +4D'y =12 x2 a. y = C, + C2x +…

A: Solved below

Q: Give the general solution of the differential equation -5x y"+ 10y'+ 25 y =3xe a) O y=C, e*+ C,xe…

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Q: Determine the solution of the differential equation 2y(4) + 3y"" + 2y´ + 6y' – 4y = 0 а. y = C¿e2x +…

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Q: Solve the linear Homogenous Differential Equations with Constant Coefficie (D' -D - 2D' +2D²…

A: The given differential equation is; (D5-D4-2D3+2D2+D-1)y=0.

Q: Find the general solution of the linear differential equations. y" - 3y' - 4y = 30e* a. y = ce4x -…

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Q: Find the general solution of the linear differential equations. (D* – 4D² ]y= 36 a. y = C, + C2x +…

A: As per our guidelines we are supposed to answer only one question

Q: Solve the ff. differential equations by applying the appropriate substitution. dy = 2+y-2x+3 1) dx…

A: Since, you have asked multiple questions as per company guidelines, we will solve the first question…

Q: Determine the solution of the differential equation y"'-6y" + 12y'-8y = 0 %3D y = C,e-2x + C,xe-2x +…

A: Given: y'''-6y''+12y'-8y=0

Q: Given the roots of a differential equation, m's 3,-2, %3D -2, -1tv2, what is the solution? y = cqe3x…

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Q: With procedure, Choose the differential equation that corresponds to the solution y = C₁e6x + ₂xе6x…

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Q: Find the general solution of the linear differential equations. y" - 3y' - 4y = 30e** a. y = (c, +…

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Q: The general solution of the differential equation x²y" - 2y = Inx is O c,x? + c2xl + 2 lnx - 1…

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Q: Find the general solution of the following homogenous differential equations: 1. (D2 + 5D + 6)y = 0…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Find the solution of the differential equation y" – 3y' + 2y = 2x3 – 9x² + 6x %3D a. y = C,ex +…

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Q: Determine the total solution of the differential equation (D2+5D+6)y=6e(-3x)-100e2x O A. y =…

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Q: The general solution to the differential equation - 2 ()- is dr = 0 is | dt3 dt2 dt O x = C1 + C2e +…

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Q: Solve the second order differential equation ý + ý - 6y = 8e* + 3x A:y = ce2x + cze-3x + 2e* + %3D 2…

A: To solve the given differential equation, first we find complementary function (C.F.) and particular…

Q: Determine the solution of the differential equation y" + 3y" – 4y' – 12y = 0 - | y = C,e2x + C2xe2x…

A: Given the differential equation is y'''+3y''-4y'-12y=0

Q: What is the differential equation of the solution y = C1e®" + C2xe®u + C3e¬7w ? O y" – 11y" + 45y +…

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Q: Solve the linear Homogenous Differential Equations with Constant Coefficients: (D' - 2D° – D+ 2)y =…

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Q: Find the general solution of the linear differential equations. y" - 3y'-4y = 30e*x %3D a. y (c, +…

A: Now first find cf and pi then write complete solution

Q: The solution of the differential equation 18 dy 24x2+9 is O 9y? = 8x3 +C O 9y = 8x2 – 9x + C O 9y? =…

A: Basics of Differential equation and Integration are used.

Q: 12) Consider the initial value problem: [ ม" - ข = - 6t? | y(0) = 5 y' (0) = 3, %3D Where y = cje' +…

A: The given problem is to find the system of linear equations for to find the solution to the given…

Q: The general solution of the differential equation x²y" – 2y = Inx is In x C1x² + c2x¬l + 1 - 2 4 1…

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Q: Determine the total solution of the differential equation (D²+8D+16)y = 64cos4x. OA.y = C₁e(-4x) +…

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Q: Solve the linear Homogenous Differential Equations with Constant Coefficients: (D° - D - 2D +2D² +…

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Q: The complementary solution of a given 2nd order non-homogeneous differential equation is yc = C1e2x…

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Q: Determine the solution of the differential equation y" - 6y" + 12y'-8y = 0 y = C,e 2x + C,xe-2x +…

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Q: Solve the second order differential equation ÿ + ỷ – 6y = 8e* + 3x 1 A:y = ce2x + c2e-3x + 2e* + 12…

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Q: What is the differential equation of the solution y = C1e 9¤ + C2xe Ya -9x + C3e7¤ ? O y" + 11y" –…

A: To find the differential equation for which the given solution belong .

Q: The general solution of the differential equation x²y" – 2y = Inx - is O C1x² + c2x¯+ In x 1 4 -2x…

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Q: What is the solution of the differential equation y" - 8y + 25y = 36e“ ? %3D O y = C1e-4 cos3x +…

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Q: Solve the given system of differential equations by systematic elimination. (D + 1)x + (D - 1)y - 5…

A: Step:-1 Given system is D+1x +D-1y=5  ----(1)6x +D+5 y =-1  ----(2) To solve this system multiply…

Q: Find the solution of the differential equation у" — 4у — 4х — Зех - y = Ce2x + C2e¯2x + e* + x а.…

A: Solution:

Q: Find the general solution of the linear differential equations. (D-4D )y= 36 a. y C, + C2x+ C3e2x+…

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Q: The differential equation a"+2x-5x sin t is equivalent to the system Sa' = 2x – 5y x = 5x -2y y =…

A: Please refer the attached image for complete solution.

Q: Find the general solution of the linear differential equations. y" - 3y'-4y = 30ex %3D a. y = Cex-…

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Q: 3 Find the solution of the differential equation (D° + 8D° + 16D)y = 0 y = C, + (C2 + C3x)cos C +…

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Q: Find three linearly independent solutions of the given third-order differential equation and write a…

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Q: What is the general solution of the differential equation: yiv + 6y''' - 39y'' - 124y' + 480y = 0…

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Q: Solve the second order differential equation ý + ý - 6y = 8e* +3x A:y = Ce2x + C2e-3x + 2e* + 2 12…

A: