Find the general solution of the differential equation y" - 6y +25y = 0. 3x ○ y = c1e³* + c2₂eª ○ y=c₁e O y = cie ○ y = c₁e¹¹ cos 3x + c₂e¹r sin 3x Oy=c₁e³ cos 4x + c₂e³ sin 4x 3x -3x + c₂e 4x cos 4x + c₂e -3 sin 4x

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A: the given equation is  y''+2y'+4=exsin2x+x2 Auxiliary equation corresponding to the equation is…

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Q: Find the solution to the differential equations sec³ xdy = csc² y dx πT y (n) == 4

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Q: Verify that the function y = x sin(x) + x cos(x) is a solution to the differential equation: y" + y…

A: 1 have verified the differential equation by finding each derivatives

Q: d²y dy d³y dx + a1' dx² + aoy = 0 dx + az° x³

A: Let y=eλxGiven: The differential equation:a3d3ydx3+a2d2ydx2+a1dydx+a0y=0To show: y is the solution…

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

A: Solved below

Q: 2. Evaluate the general solution of the differential equation using the variation of parameters…

A: Given, x'' + 4x = sin2 2tor    d2xdt2 + 4x = sin2 2t or     D2 + 4x = sin2 2t Here auxiliary…

Q: The complementary function(C.F.) of the differential equation (D2 + 6D+ 18)y= z is_

A: In this question, we have find the complementary function for the differential equation.

Q: y-3y+2y=2x +sin x+(1+2x)e" +4e* %3D

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Q: The complementary function(C.F.) of the differential equation(D – 2)°y = sin 2x is_ O (ci + c2x +…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: What is the complementary solution y, for the differential equation y"- 4y=12x A y,=c,cos 2x + c,sin…

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Q: Find a particular solution to the differential equation y" + Oz/ – 16y = -768t°.

A: Given: y'' + 0y' - 16y = -768t3

Q: What is the solution of the differential equation 20분 +3분+2분 +6-4y=0? Oy=C₁e¹2 + C₂e²+ C3 cos √r –…

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Q: Make the Nonexact differential equation xy dx + (3y2 + 2x2 – 20) dy = 0 to an exact differential…

A: The solution is given as

Q: Verify that the indicated expression is an implicit solution of the given differential equation. 1 (…

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Q: The complementary function(C.F.) of the differential equation(D – 7) (D+4)y= 7x is_ O (ci + c2x)e +…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Determine the solution of the differential equation dy cos? x sinx dx + (cos³ x)y = 1 a. y = tanx +…

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Q: dy What is the general solution to the differential equation dx cos x+sin x 2y for y > 0 ? A cos…

A: topic - differential equations

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Q: Determine the general solution of the differential equation y" + 4y = sin(3t).

A: Given differential equation: We have to determine the general solution of the given differential…

Q: What is the solution of the differential equation (D³ +2D² +D+2) y=0? Oy=C₁e²+ C₂ cos x + C3 sin x…

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