# 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 Preview

1. Solve the following differential equation:

We have ,

. This can be solved by using variables separable method.

Integrating, we get is the ...

#### Solution Summary

Differential equation is reiterated. The area of bounded regions are determined.

$2.19