The general solution to the differential equation -9x²y" + 9xy' - 18y = 0 is given by: A) C;(cos x)e+ E2(sin x)e (B) C1x cos x + C2x sin x (C) C¡ cos x + C2 sin x D) C1x cos(ln x) + C2x sin(ln x) (E) C1 cos(ln x) + C2x

Q: (b) у" — 2у + у 3 еt sin(z)

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A: Consider the provided differential equation,

Q: Solve for the differential equation

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A: We will solve the given linear differential equation by finding Complementary and particular…

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A: The solution is given as

Q: Form the differential equation for the function x +2y = a sin3x - bcos3x а. Зу" - 18у %3D -9х O b.…

A: The second order differential equation for a function can be found by differentiating the function…

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Q: a) Solve differential equation dx + 2 dy x³ cos y %| - y

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Q: Solve the equation y' + a = eax +)csc(ax+y), where a is a real number Select one: a. e-(x…

A: The differential equation is given as y'+a = e(ax+y)csc(ax+y)                          (1) Let ax+y…

Q: Use variation of parameters to solve the differential equation x²y" + 10xy' + 8y = x².

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Q: (r+sin 0- cos 0) dr + r (sin 0 + cos 0) d0 = 0

A: (r+sinθ-cosθ)dr+r(sinθ+cosθ)dθ=0 lets rearrange and then integrate

Q: solution to this differential equation: (y3sec2x)dx - (1-2y2tanx)dy = 0

A: The given DE is: y3sec2xdx-(1-2y2tanx)dy=0 So, let  M=y3sec2x, N=-(1-2y2tanx)So, My=3y2sec2x,…