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    © BrainMass Inc. brainmass.com December 24, 2021, 5:01 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/solve-equation-functions-21879

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    SOLUTION This solution is FREE courtesy of BrainMass!

    Given,

    Y'''' - 2 Y ''' + 2 Y'' - 2Y' + Y = 0 ---(1)

    Theorems to be used.
    a) y' ---> d/dx (y)
    b) d/dx (Y^n) = n Y ^ (n-1)
    c) Integration of (Y') = Y
    d) Integration of (Y^n) = (Y^n+1)/n+1
    e) Integration of (Constant) = Y

    Integrating (1) by using the above theorems

    Y''' - 2 Y '' + 2 Y' - 2Y + (y^2)/2 = 0 ---(2)

    Integrating (2) by using the above theorems

    Y'' - 2 Y ' + 2 Y - Y^2 + (y^3)/6 = 0 ---(3)
    Integrating (3) by using the above theorems

    Y' - 2 Y + Y^2 - Y^3/6 + (Y^4)/24 = 0 ---(4)

    Integrating (4) by using the above theorems

    Y - Y^2 + Y^3/3 - Y^4/24 + (y^5)/120 = 0 ---(5)

    Solving the above equation,

    Y^5 - 5Y^4 + 40 Y^3 - 120Y^2 + 120 Y = 0

    This is the final answer.

    Hope this helped

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:01 pm ad1c9bdddf>
    https://brainmass.com/math/basic-algebra/solve-equation-functions-21879

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