, It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear. Linearity is important because the structure

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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It can be helpful to classify a
differential equation, so that we can predict
the techniques that might help us to find a
function which solves the equation. Two
classifications are the order of the equation --
(what is the highest number of derivatives
involved) and whether or not the equation is
linear .
Linearity is important because the structure
of the the family of solutions to a linear
equation is fairly simple. Linear equations can
usually be solved completely and explicitly.
Determine whether or not each equation is
linear:
?
1.
y" – y + y? = 0
?
2.
y" – y+ t² = 0
?
3.
d²y
+ sin(t + y) = sint
dt2
?
4.
dy
+ ty? = 0
dt
Transcribed Image Text:It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear . Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear: ? 1. y" – y + y? = 0 ? 2. y" – y+ t² = 0 ? 3. d²y + sin(t + y) = sint dt2 ? 4. dy + ty? = 0 dt
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