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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.

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## 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) = axÂ² , a>0 , and g(x) = xÂ³

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!

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