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: 2nd order Nonlinear 1. "-y + y² = 0 2nd order Linear 4th order Linear 2. 3. d²y dt² + sin(t + y) = sint d'y d³y d²y dy + + dt4 dt3 dt² dt d²y 2nd order Nonlinear 4. (1+²) +t dy dt2 dt + = 1 +y=e
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: 2nd order Nonlinear 1. "-y + y² = 0 2nd order Linear 4th order Linear 2. 3. d²y dt² + sin(t + y) = sint d'y d³y d²y dy + + dt4 dt3 dt² dt d²y 2nd order Nonlinear 4. (1+²) +t dy dt2 dt + = 1 +y=e
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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Which one is wrong here?

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:
2nd order Nonlinear
2nd order Linear
4th order Linear
2nd order Nonlinear
1. y" -y + y² = 0
d²y
dt²
2.
3.
+ sin(t + y) = sint
d¹y d³y d²y dy
+
+
dt4 dt3 dt2 dt
d²y dy
4. (1+²) +t
dt² dt
+ = 1
+y=et
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