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1.(Easy) For the following differential equations, state the independent and dependent variables, the order, the degree, and say whether the ODE is linear or nonlinear: (a) cos(x) y" + 5y' + 8xy = tan x. (b) x4d°y – 8 (O" + y = 0. - dr³ dx (c) sin(t) y – tôy" +1 = 0. (d) +- d4u dr4 d2u dr2 cos(r + u). + u = d³y dx5 = (1+ y³)!/3. (f) ä – i² + x = 0. (e) (Warning: Half of these examples have degree = ∞.)

1.(Easy) For the following differential equations, state the independent and dependent variables, the order, the degree, and say whether the ODE is linear or nonlinear: (a) cos(x) y" + 5y' + 8xy = tan x. (b) x4d°y – 8 (O" + y = 0. - dr³ dx (c) sin(t) y – tôy" +1 = 0. (d) +- d4u dr4 d2u dr2 cos(r + u). + u = d³y dx5 = (1+ y³)!/3. (f) ä – i² + x = 0. (e) (Warning: Half of these examples have degree = ∞.)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1.(Easy) For the following differential equations, state the independent and dependent variables, the order, the degree, and say whether the ODE is linear or nonlinear: (a) cos(x) y" + 5y' + 8xy = tan x. (b) a4 – 8 (´+y = 0. - dx3 dx (c) sin(t) y – tôy" +1 = 0. (d) + + u = cos(r + u). du dr4 d²u dr2 (e) = (1+ y³)'/3. d°y dx5 (f) ï – x² + x = 0. (Warning: Half of these examples have degree = .)
Transcribed Image Text:1.(Easy) For the following differential equations, state the independent and dependent variables, the order, the degree, and say whether the ODE is linear or nonlinear: (a) cos(x) y" + 5y' + 8xy = tan x. (b) a4 – 8 (´+y = 0. - dx3 dx (c) sin(t) y – tôy" +1 = 0. (d) + + u = cos(r + u). du dr4 d²u dr2 (e) = (1+ y³)'/3. d°y dx5 (f) ï – x² + x = 0. (Warning: Half of these examples have degree = .)
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