D. Use Variation of Parameter: Solve the equation: (D² – 3D) + 2y : e 2x 1+e2x

Q: Q58- By using Frobenias motheed Solve ovi 6x?C _x) Y+ 12x² (1+x}Ý -Cal-x')y=o

A: Given: 6x31-xy''+12x21+x3y'-21-x2y=0 To find: Solving ODE by using Frobenius method.

Q: FIND THE GENERAL EQUATION OF THE FOLLOWING SOLUTION: y" = 12 %3D A.

A: A) The differential equation is given as y''' = 12 On integrating both sides , we get ∫y''' = ∫12y''…

Q: 2x+2y=18 x=3-y  What is the solution as a coordinate?

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Q: 3) (G) (H) 2D + 11D + 18D² + 4D - 8 = 0

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Q: O+3D+a)= -2x t. Ae y=

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Q: Find the Solution of the ff: 1. (D³ – 3D² – 3D + 1)y = 0

A: As per our guidelines we are supposed to solve only one question i.e. the question no (1). For the…

Q: Solve (D3 – D?)y =0 O a. y = cqe0x + C2e* O b. y = C1+ C2x + C3e* O c. y = C1+C2X + C3e¬* * + c,e+ O…

A: The given homogeneous differential equation is: (D3-D2)y=0 The characteristic polynomial is: λ3-λ2…

Q: pls solve the DE: a) y''+10y'+25y=0, y(0)=5, y'(0)=−19 b) y''−6y'+10y=0

A: In the given question we have top solve the differential equations s.t  (a) y''+10y'+25y=0 with the…

Q: Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the…

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Q: Solve (D- 1)'y=o O a. y = ce+C2xe+ c36 O b.y= c,e *+c,xe *+ + C,xeX + O c.y = C1e -

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Q: Q2\Using the variation of parameter, find the solution of: y'+25y = csc 5x %3D

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Q: Solve the d.e. using Method of Undetermined Coefficients (MUC) (D² – 3D – 4)y = 30e4x ||

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Q: The position of a particle is given by s(t) 2t3- 12t2 +18t, %3D is in seconds.

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Q: Q2\Using the variation of parameter, find the solution of: y'+16y = csc 4x

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Q: D.E Solve the Fo llowing %3D

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Q: Find the solutions of the equation in the interval [-2n, 2n]. csc(x) = V2 %3D

A: Since you have asked multiple questions, we will solve the first question for you . take…

Q: Solve using the parameter variation method. w''+2w'−3w=8e-t/(1+e2t)

A: The solution is given as

Q: . Use variation of parameters to solve 4y" + 36y = csc(3x).

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Q: Q. Solve the equation using Variation of Parameters: y" – 5y' + 4y = x. -

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Q: du Solve the equation "u(0, y) = 8e» = 4. by the method of separation of variables.

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Q: Solve the DE using the method of variation of parameters: x²y" – 4xy' + 6y =30x³, y(1) =5 , y’(1) =5

A: homogeneous system is  compare this equation with  so here we have

Q: Q9. Solve (x3 + уз)dy + x2y dх %3D0

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Q: 3) Solve dAfferentral equation.(b and the variables ) are (D2+ 4D+3)b = 1+ 2g +3a ²

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Q: Find the solution of dy r(1+ y?) dr 4+22

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Q: (5x2 – y²) dx + 2ydy = 0

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Q: solve for y in terms of t or x, as appropriate.

A: 1. e5k = 1/42. 80 ek = 13. e(ln0.8)k = 0.8

Q: 3. f(x) = a = 4 %3D V-2

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Q: The foci of the below equation are x² – 4y² + 2x + 8y – 7 = 0

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Q: a) For x 2 0, which equation is false? (xi)* = V Vx3 (1) X2 %3D

A: For (1),  x232=x43=x43

Q: Solve the equation by using the method of variation of parameters dy 2dy 22 + 2y = e“ csc x. dx dx2

A: Let us consider the second order differential equation y''+py'+qy=g(t) Determine the complementary…

Q: Squaring both sides of the equation gives that r +s = r+ 2vrVs+ s.

A: Given: The statement,

Q: Q2\Using the variation of parameter , find the solution of: y'+9y= sec3x

A: Particular solution by variation of parameter where W is wronskian of y1 and y2.

Q: Solve the equation: W = ;a – 3d for a. Oa = 2W + 3d Oa = W+3d 2 Oa = 3wd 2

A: We have to solve for a

Q: y" – 6y' + 9y = :

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Q: Solve the IVP: y" + y = 6(t – 2m), y(0) = 0, y (0) = 1.

A: y“+y=δt-2π

Q: a) Find the general solution of the equation d'y dy dr? + 3e* dr by using the method of undetermined…

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Q: Find the general solution. Provide complete and neat solutions. (D⁴ + 2D² + 1)y = 0

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Q: b. Solve by using the method of variation of parameter 3x y"-6y'+9y= y(1) = 1; y '(1) = 2

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Q: 3. Find all solutions to the equation (D² – 3D + 2)y(x) = 2e3ª.

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Q: What is the degree of the differentia equation dy 5a4 – 6x2 ? dx3 .A 1 .B .C 4 .D

A: The degree of the differential equation is represented by the power of the highest order derivative…

Q: Solue the differantial equation Dxy'+3y=6x3

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Q: Solve the given DE using the method of undetermined coefficients. (D² + 3D+2) y = 12x2

A: Let's find.

Q: Differntiate the equation implicity to find p' (x). r'p+xp+1 2x+p 3D1

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Q: What are the foci points for the equation 36x2 + 25y² – 144x – 50y – 731 = 0?

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Q: 2y"+18y=6tan(3t)

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Q: b. Solve by using the method of variation of parameter 3x y"-6y'+9y =;y(1) = 1; y '(1) = 2

A: Solving question number B.

Q: Solve (D – D4 + 4D³ – 4D²) y = 32 cos (2x) – 20e¬× %3D

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Q: 2y"+18y=6tan(3t)

A: Given differential equation is  2y"+18y=6tan3t

Q: Given the equation: y = (eln x², find y. A In x B 2(In x) / x (c) 2x D 2 elnx

A: