Given the differential equation + 9D + 27D+ 27) y= In(2x – 3). Propose an appropriate particular solution. Take A, B and C to be functions of Yp Axe-3r + Bx²e-3¤ + Cx³e-3r Ур = Ae-3* + Bxe-3* + Cx?e-3# Yp = Ae-3x + Be-3* + Ce-3x Yp = Ae3* + Bæe3* + Cx²e3*

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Q: c. x²y″ − 3xy' +4y=0, _y(1)=5, y′(1)=3. - - d. x²y" — 5xy' + 8y =8x6, y(½)=0, y′(½¹⁄) = 0.

A: (c) A differential equation is given by, x2y''-3xy'+4y = 0 with initial conditions y1 = 5 and y'1 =…

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

Q: The general solution of the differential equation x2y′′+xy′+(25x2−9)y=0x2y′′+xy′+(25x2−9)y=0 is?

A: The differential equation of the form  x2y''+xy'+x2-ν2y=0            i is referred to as Bessel's…

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A: We will find out the required differential equations for given roots of auxiliary equation.

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A: y''-36y=0auxillary equation is given bym2-36=0(m+6)(m-6)=0m=-6,6m1=6 , m2=-6

Q: =C2e(-2x) - 6xel-3x) - 5e (2x) + C₂e(-2x) + 6xe(-3x) + 5e (2x)

A: option A is correct answer

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A: We can solve this problem by applying the concept of linear differential equation.

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A: we are given the solution of the differential equation as  y=c1e9t+c2e-3t

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A: Given, y''-2y-15y=18e6x Particular solution: ypx=2e6x

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A: Use the cauchy Euler method to solve this problem.

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A: We need to find auxiliary equation.

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A: The solution of given question is given as follows:

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A: Given:       3x2y-4xy3+6xdx+x3-6x2y2-1dy=0 Here M=3x2y-4xy3+6x            N=x3-6x2y2-1

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A: Solution:

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Q: Find a differential equation for y=c1e^9t +c2e^-4t. Oy"+5y'+16y=0 Oy"-5y'-16y=0 Oy"+5y'+36y=0…

A: Find DE