mathematics

Problem set # 1

1. Find the general solution of the differential equation:

xyyy 2sin2 

2. Change the order of integration

   



9

7

10

/9

7

3

3

/9

),(),(

x

xx

dyyxfdxdyyxfdx

3. Find the interval of convergence of the series  

 

 



1 2

2

1

n n

n

n

x

4. Find the general solution of the differential equation

x

xeyy 2 .

5. Determine whether the series  

   

 



1

2

!12

1

n n

n is convergent or divegrent.

6. Evaluate the double integral   D

yxa 222

in polar coordinates. The

domain D is bounded by the curves )0(2,0 22

 yaxyxy .

Problem set # 2

1. Find the interval of convergence of the series

 

 









1

12

149

1

n n

n

n

x .

2. Find the general solution of the differential equation

xyyy 432 

3. Find the general integral of the differential equation

  05 22  dxyedye xx . .

4. Change the order of integration

 x

x

dyyxfdx

3

2

1

0

),(

5. Find the Taylor series of the function   6

4

 

x xf about 5

0 x

and find its radius of convergence.

6. Calculate the integral   D

dxdyyx )2( where the domain D is bounded

by the curves 2

xy  and xy  .