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 + y² = 0 d'y dt2 2. + sin(t + y) = sint d'y d³y d²y dy + + dt4 dt3 dt2 dt d²y dy dt2 dt 4. (1+²) + + = 1 +y=et
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 + y² = 0 d'y dt2 2. + sin(t + y) = sint d'y d³y d²y dy + + dt4 dt3 dt2 dt d²y dy dt2 dt 4. (1+²) + + = 1 +y=et
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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:
2
?
?
2
V
1. y" -y + y² = 0
2
3.
d²y
+ sin(t + y) = sint
dt²
d¹y d³y d²y dy
+ +
dt4 dt³ dt² dt
d²y dy
dt
dt²
4. (1+²) +t
+ = 1
+y=et
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