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    Solving differential equation using modified Euler's method.

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    Use the modified Euler's method to solve y' = -y +x + 2; y(0) =2 on the interval [0,1] with h = 0.1

    Carry all computations to three decimal places.

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    https://brainmass.com/math/calculus-and-analysis/solving-differential-equation-using-modified-eulers-method-114521

    Solution Preview

    Here f (x, y) = -y+x+2, x0 = 0 and y0 = 2, and we are to use h = 0.1. We begin by approximating the value of y at x1 = x0 + h =0.1. A first approximation y1(1) to this value is found using the formula,
    y1(1) = y0 + h f (x0,y0) = 2.000 +0.1 (-2.000+0.000+2.000) = 2.000
    We now find the second approximation y1(2).
    Since f (x1,y1(1)) = f (0.100, 2.000) = -2.000+0.100+2.000 = 0.100

    y1(2) = y0 + ½ [f ...

    Solution Summary

    Solving differential equation using modified Euler's method.
    We begin by approximating the value of y at x1 = x0 + h =0.1. A first approximation y1(1) to this value is found using the formula,
    y1(1) = y0 + h f (x0,y0)

    $2.19