1. For the following differential equations, specify the independent and dependent variables, state the order, and say whether the ODE is linear or nonlinear: (a) (1 – r)y" – 4ry+5y = sinx. 5 (b) xdy − (dy)³ + y = 0. (c) t5y-t³y + 6y = 0.
1. For the following differential equations, specify the independent and dependent variables, state the order, and say whether the ODE is linear or nonlinear: (a) (1 – r)y" – 4ry+5y = sinx. 5 (b) xdy − (dy)³ + y = 0. (c) t5y-t³y + 6y = 0.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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Please help with the following questions.
Transcribed Image Text:1. For the following differential equations, specify the independent and
dependent variables, state the order, and say whether the ODE is linear
or nonlinear:
(a) (1 — x)y"" — 4xy + 5y'
-
5
(b) x² - (dy)³ + y = 0.
(c) t5y-t³y + 6y = 0.
(d) + +u = sin u.
dr2 dr
(e)
+ (dy) ²2.
(f) x
(1 + x³) x - x.
(g) (sin)y"" (cos 0)y = 9.
=
=
=
sin x.
(Note: Since the word "degree" is ambiguous with at least four
competing definitions, I am not asking you about the "degree" of the
ODE.)
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Could you please do the remaining 4 questions (1d, 1e, 1f, 1g). It is in the image.
Transcribed Image Text:1. For the following differential equations, specify the independent and
dependent variables, state the order, and say whether the ODE is linear
or nonlinear:
(a) (1 − x)y" – 4xy+5y = sin .
(b) x dy
d²y
(c) t5y" - t³y + 6y = 0.
(d) du +u =
d²
du
dr
dr2
d²y
dx²
5
(dy) + y = 0.
=
sin u.
2
√₁+ (du) ².
1
(e)
(f) = (1+³)i — x.
-
*x*
(g) (sin)y"" - (cos) y = 9.
(Note: Since the word “degree" is ambiguous with at least four
competing definitions, I am not asking you about the "degree" of the
ODE.)
Solution
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