Differential Equation d²y dx² 1) d³ y dy dx3 dx 2) (D³ + 3D² 4D - 12) y 3) 2D4 +11D³ + 18D² + 4D 8 = 0 = = Auxiliary Equation O(A) (D) (G) Roots (B) (E) (H) General Solution (C) (F) 1)

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A: These questions are about ordinary differential equation.

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A: Given differential equation:- 6x+y2dx+y2x-3ydy=0

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A: If the roots m1,m2,...,mn of the Auxiliary equations are distinct and real then the complete…

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A: Solution is given below:

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A: Note: according to our guidelines we can answer only first question because there are multiple…

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A: Here we have to solve the differential equation.

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A: Given : i) (D2+16)y=tsint ii) (D2+D+5)y=tcos2t.

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A: Topic = Differential equation

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A: According to our guidelines we can answer only one question and rest can be reposted.

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A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Q2) An integrating factor of (x²+e³)dx + (e³ + 2ye¯)dy = 0 is = (A) e-* (B) e (C) e- (D) e (E) e-2x

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Solve y" -6y"+ 2y' + y = 0 . You may use Mathematica for solving the characterestic equation!

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