MAT187H1 Lecture 15: 8.4 First Order Linear DEs & 8.5 Modelling with DEs

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MAT187H1Lecture158.4FirstOrderLinearDEs&8.5ModellingwithDEs
Examinebehaviour
y(t)=Ce
kt
b/k
Case1 y,k,b≠0
dt
dy =k+b > 0
(t)ey=ckt +k
b
a) ( )y=k
b
dt
dy = 0
y
dt
dy =k+b=kk
b+b= 0 dt
dy = 0
b) , ky y ,b yy <k
b < b  − k+b> 0 k> 0
y,ieslope
dt
dy =bk> 0 > 0
c) y,ky yy >k
bk>b b> 0  − k+b< 0
y,ieslope
dt
dy =k+b< 0 < 0
GeneralSolution
yyy
dt
dy =k+b=k+b
 
slopefield;directionfield
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