For each of the differential equation determine the order of the equation and if the equation is linear or nonlinear. (a) +2d²y + t dt² dy dt + 2y = sint 2nd order linear (b) (1 + y³)²y dy + t +y = e¹ 2nd order ✓ dt² dt nonlinear d'y (c) d³y d'y dy + + y = 10 4th order dt4 dt³ dt² dt (d) + ty = 0 1st order dt d'y (e) + sin(t + y) = sint dt² d³y (f) dt3 dt nonlinear 2nd order ✓ 3rd order + (cos²t)y = 1² nonlinear linear linear

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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For each of the differential equation determine the order of the equation and if the equation is linear or nonlinear.
(a) +2d²y
dy
dt
+ 2y = sint 2nd order
dt²
linear
(b) (1 + y³)²y
dy
+ t +y = e¹ 2nd order ✓
dt²
dt
nonlinear
d'y
d³y d'y
dy
(c)
+ y = 10
4th order
dt4 dt³ dt²
dt
(d) + ty = 0 1st order
dt
d'y
(e) + sin(t + y) = sint
dt²
d³y
(f)
dt3
+ t
dt
+
nonlinear
2nd order ✓
3rd order
+ (cos²t)y = 1²
nonlinear
linear
linear
Transcribed Image Text:For each of the differential equation determine the order of the equation and if the equation is linear or nonlinear. (a) +2d²y dy dt + 2y = sint 2nd order dt² linear (b) (1 + y³)²y dy + t +y = e¹ 2nd order ✓ dt² dt nonlinear d'y d³y d'y dy (c) + y = 10 4th order dt4 dt³ dt² dt (d) + ty = 0 1st order dt d'y (e) + sin(t + y) = sint dt² d³y (f) dt3 + t dt + nonlinear 2nd order ✓ 3rd order + (cos²t)y = 1² nonlinear linear linear
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