To find the differential equation of y= c,e 2x c e“ cos 3x + c,e“ sin 3x, we use elimination of constants. If by getting the first derivative, we arive at y'e-2* - 2ye- — 3 с, sin 3 x + 3с, сos 3 х, which of the differential equations is correct? у" — 13 у' + 4y %3D 0 у" — 4 у' + 13 у %3D0 У'+ 13у — 4у %3D0 у" + 4у' — 13 у %3D 0

Q: 7) Determine the particular solution to the differential equation y 3x-2 that passes through the…

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Q: dy 4. x - y = x² sin x dx

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Q: Tell whether x = C1et + C2 cos 2t + C3 sin 2t is a solution to the differential equation x''' - x''…

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Q: (b) у" — 2у + у 3 еt sin(z)

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Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: We first obtain Dy, D2y, D3y, D4y, D5y for given particular solution y. Then we find which of the…

Q: Find the solution of the following Differential Equations 1 В) у+-у-17 sin(2t), y(0) = -1.

A: Note:  We'll answer the first question since the exact one hasn't specified. Please re-submit the…

Q: (16x y² exy + y sec² (xy) - 2x + 3y) + (16x² y e4xy + x sec² (xy) + 3x)y' = 5

A: Let us consider the equation Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x The solution of the…

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Q: 70. 4y" +5y' - 2y = e²+xsinx

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Q: 3.- Show the differential equation is exact, then solve the equation. dy _ 3x2 - 6ху Зx? — у dx

A: To show that the differential equation is exact and to find the general solution

Q: Solve each differential equations by integrating factors or reducing equations in exercises.

A: We will find out the required general solution.

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Q: dy _ x? +y° ,2x,2y+ 2 Solve the differential equation: dx ху,х,у+1

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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…

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Q: Solve the differential equation (x – 3y + 2) dx + (3x + 9y – 12) dy = 0

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Q: y(5)_y(3) = e²+2x²-5 y(4) + 5y" + 4y = sinx + cos2x

A: Given: The equations are y5-y3=e2+2x2-5 and y4+5y''+4y=sin x+ cos 2x. The objective is to find the…

Q: 2) Find the general solution of the equation 1 y""+y' = (sinx)3

A: The  given equation  is  The auxiliary  equation is  given by…

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Q: Use the differential operators method to solve the equation y"-5y'+6y = e* .A y =ce2x+c,e3x + 2x .B…

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Q: Given the differential equation: D´(sin x- cos x+ 3e* +x²) What is the fourth derivative? a - sin…

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Q: The complementary function(C.F.) of the differential equation(D – 3)°y=sin 3x is O (ci + c2z +…

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