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    Differential equation

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    1. Solve the following differential equation:

    -2yy' +3x^2 SQRT(4-y^2) =5x^2 SQRT(4-y^2) , -2 < y < +2

    2. Let f(x) = ax^2 , a>0 , and g(x) = x^3

    Find the value of a which yields an area of PI (i.e. 3.14159) for region bounded by figure, y-axis and line x=1.

    © BrainMass Inc. brainmass.com December 24, 2021, 8:55 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/differential-equation-area-bounded-region-326572

    SOLUTION This solution is FREE courtesy of BrainMass!

    1. Solve the following differential equation:

    We have ,
    . This can be solved by using variables separable method.
    Integrating, we get is the solution for the differential equation.

    2. Let f(x) = ax² , a>0 , and g(x) = x³

    Find the value of a which yields an area of (3.14159) for region bounded by figure, y -axis and line x =1

    We first find the intersection points. They are given by
    We set up the function as integrand for the area. As the curve f(x) is touching the curve g(x) at origin, its graph will be always above the graph of g(x).
    Given that the area covered is . Hence we have
    Hence the approximate value of a is 2.47

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

    © BrainMass Inc. brainmass.com December 24, 2021, 8:55 pm ad1c9bdddf>
    https://brainmass.com/math/calculus-and-analysis/differential-equation-area-bounded-region-326572

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