Unformatted text preview: t
+ y = sin(t)
dt
2 dy
t
+ y 2 = sin(t)
dt r2
= rP − P
K < Nonlinear < Linear < Linear Classifying DEs (Section 1.3)
• Linearity  a DE is linear if it is linear in the unknown function and all its
derivatives.
• (A) Linear or (B) nonlinear: dP
= rP
dt P
1−
K d4 w
EI 4 = q
dx
2 dy
t
+ y = sin(t)
dt
2 dy
t
+ y 2 = sin(t)
dt r2
= rP − P
K < Nonlinear < Linear < Linear
< Nonlinear More deﬁnitions  solutions More deﬁnitions  solutions
• Solution to a DE on some interval A More deﬁnitions  solutions
• Solution to a DE on some interval A
• a function that is suitable differentiable everywhere in A (i.e. has as
many derivatives as appear in the equation) and, More deﬁnitions  solutions
• Solution to a DE on some interval A
• a function that is suitable differentiable everywhere in A (i.e. has as
many derivatives as appear in the equation) and,
• satisﬁes the equation. More deﬁnitions  solutions
• Solution to a DE on some interval A
...
View
Full
Document
This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at UBC.
 Spring '13
 EricCytrynbaum
 Math, Differential Equations, Logic, Equations, Partial Differential Equations

Click to edit the document details