Apply Euler's method twice to approximate the solution to the initial value problem on the interval 0. first with step size h=0 25, then with step size h= 0.1. Compare the three-decimal-place values of the two approximations at x =- with the value of y of the actual solution. y'=y-3x-3, y(0) - 5. yox)= 6+ 3x- e

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A: x1 - x2 + 1 = 0  =>  x1 = x2 - 1  x12 + x22 = 4 =>  x2 = (4 - x12)1/2    x1(0) = 0.8, x2(0) =…

Q: 1. Solve y"+8y'+16y= 4e ||

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Q: please use the method of variation of parameters to determine the particular solution y'"+30y"…

A: The given differential equation is:y'''+30y''-4000y=e-20x

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Q: Q 2- use Newton-Raphson method to obtain a root of equation x'- 2x + 3x -5 = 0 %3D

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Q: 5. [10 points] Find the general solution y"-6y' +9y = x*e*

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Q: How do I find the particular solution yp in the equation above?

A: For particular equation we will crate function for particular integral. Then we solve it by using…

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Q: 2. Use the variation of parameters to solve: y" -2y" + y' = 4e*.

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Q: 5. Solve, using the method of undetermined coefficients: y" + 2y' = 2x + 5 – e-2= %3D

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Q: 1. Solve the IVP. (xy2 + 3y2)dy-2xdx = 0 y(-4)=-3/18 2. Solve the IVP. y" +2y+2y=8(t- -플) y(0) = 3,…

A: 1. 2. 3. 4. 5. 6. 7. 8. 9.

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Q: Solve the following initial value problems: (y + 2y - 3y = u(t-1)-u(t-3), y (0) = 0, y'(0) = -1.

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Q: Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with step size…

A: Solution:   Given IVP is y1=y-2x-4 , y0=3 x∘=0,  y∘=3, h=0.1 , xn=0.5∴fx,y=y-2x-4Formula:…

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