Transcript Section 11.4 Separation of Variables

Section 11.4
Separation of Variables
• Recall our yam differential equation and
solution
dT
 0.025(200  T )
dt
T  200  Ce
0.025t
• We have already verified that this is a solution
• Now we will look at how to solve this using
separation of variables
– Basically we will separate the t’s from the T’s
Exponential Growth and Decay Equations
• We often have differential equations of the
form
dy
 ky
dx
• Let’s solve this with separation of variables
Examples
dy
1)
 .2 x, y  6 where x  1
dx
dP
2)
 P  4, P  100 when t  0
dt
dz
2
3)
 z  zt , z  5 when t  0
dt