Separation of Variables, solution to problems in the book. This slide presentation accompanies my lecture in differential equations.

1. Solutions to solved problems

2.   


ckdxydy
kdxydy
kdxydy
y
k
dx
dy
0 ckxyckx
y
 2or
2
2
2
Guide

3.     22
1'1 y
dx
dy
xyyx 
Guide
 
 
0
1
1
2
2





x
dx
y
dy
x
dx
y
dy
cx
y
c
x
dx
dyy







 
1ln
1
1
1
2
ycxy
cx
y


1ln1
1ln
1
  11ln  cxy
Pareho lang yan

4. Guide
0

x
dx
y
dy
x
dx
y
dy
x
y
dx
dy
cxy
c
x
dx
y
dy

 
lnln
cxyc
x
y
cee cxy

lnln

5. Guide
 
  dxxdyy
x
dx
dy
y
2
2
1
1


 
cxyy
cdxxdyy

 
3
3
12
2
1
2
1
cxyy  32
236

6. Guide
0
sin
cos
cos
sin
 dy
y
y
dx
x
x
cyx
cdyydxx

 
sinlncosln
cottan
xcy
c
x
y
ce yx
cossin
cos
sin
sinlncosln




7. Guide
  

cydyyxdx
dy
y
y
xdx
tansec
0
cos
tan
2
2
cyx
cyx


22
2
2
12
2
1
tan
tan

8. Guide
   
cdyydxxx 2
ln
c
y
xxx 
1
2ln2 22