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# differential equation

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1. Solve the following differential equation:

-2yy' +3x² √(4-y²) =5x² √(4-y²) , -2< y<+2

2. A calculus instructor has determined that the arc of an individual diving into a swimming pool is defined by the function, f(x) = sin (.4x). Determine how far the diver has traversed in his dive as he passes through the imaginary plane created by extending the diving board horizontally. ( Hint: consider the edge of the diving board to be origin of the coordinate system and use the arc length formula.)

3. Define a region bounded by f(x) =2x³ , g(x) = 3-x², and the y-axis. Find the volume of the solid generated by revolving the region about the line y =3 utilizing the shell method. (Can you also try to do this using the disc method to see if it works both ways.)

4. Integrate the following function:

7/x²+6x+13 (Hint: 13=9+4 ; x²+6x+9 is a perfect square substitute

of 7/x²+6x+13 )

##### Solution Summary

The expert discusses differential equations function for regions bounded in a graph. Differential equation functions for regions bounded are determined.

##### Solution Preview

1. Solve the following differential equation:

We have ,
Integrating, we get is the solution for the differential equation.

2. A calculus instructor has determined that the arc of an individual diving into a swimming pool is defined by the function, f(x) = sin (.4x). Determine how far the diver has traversed in his dive as he passes through the imaginary plane created by extending the diving board horizontally. ( Hint: consider the edge ...

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