mathematics

Problem set # 1

1. Find the general solution of the differential equation:

xyyy 2sin2 

2. Change the order of integration

  





9

7

1

0

/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  .