Given, x = c, cost+c, sint is a two-parameter family of solutions of the second-order DE x'"'+x = 0. Find a particular solution of the second-order IVP consisting of this DE and the given initial conditions: (a) x(0) = -1, x'(0) = 8 (b) x(7/2) = 0, x'(x/2)=1 (c) x(7/6) =, x'(T / 6) = 0 2 (d) x(7/4) = V2, x'(7 /4) = 2/2 %3D

Q: B. Solve x' = 01 1 54 x + 12e4t 18e4t

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Q: (x^2)y''-2xy'+2y=0; y(1)=4, y'(1)=7   Find particular solution that satisfies the given condition

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Q: Given f(x) = In(- 4e" – 13), f'(x) = %3D

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Q: 2- y'" + 7.5y" + 14. 25y' – 9.125y = 0, y(0) = 10.05, y'(0) = -54.975, y"(0) = 257.5125 %3D %3D…

A: As per answering guidelines of Bartleby I am supposed to answer only first question. If you want…

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Q: Show that each of the functions on the left is a 3-parameter family of solutions of the DE on its…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: First, solve the following IVP, y' = (15x + yr1 . 15 , y(0)=1. Then calculate y(12).

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Q: The general solution of x' = 2x + 5y and y' = -2x - 4y

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Q: Solve for y(x):  y’’ – 5y’ + 12y = 0; y(2) = 0; y’(2) = -4

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Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

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Q: Set up the appropriate form of a particular solution yp of the dif- ferential equation…

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Q: of y' = x²/(y + 1)?

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Q: Can you elaborate how to incorporate c into the solution. Like c=0? And how does f'(0)=7 and…

A: Solution below

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A: differential equation

Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

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Q: Solve IVP: y'''+4y'=x, y''(0)=1; y'(0)=0.

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Q: Solve the following 2nd order D.E using variation of parameters method: y'' + 2 y' + y = e^(-x)

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Q: Find ect and the solution to X' = CX + (1) t X (0) = 0

A: X'=CX+1t1X0=000

Q: [  y'''- y' = ex - 2x  ] Please find a particular solution yp for the above.

A: Particular Solution: Consider the equation Let be the differential operator Then equation (1) can…