# Differential equation

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

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