6 Determine whether any of the functions (a) y₁ = sin 2x, (b) y₂(x) = x, or (c) y3 (x) = sin 2x is a solution to the initial-value problem y" + 4y = 0; y(0) = 0, y (0) = 1.
6 Determine whether any of the functions (a) y₁ = sin 2x, (b) y₂(x) = x, or (c) y3 (x) = sin 2x is a solution to the initial-value problem y" + 4y = 0; y(0) = 0, y (0) = 1.
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...
Related questions
Question
#6
![1 Find the explicit solution to the equation
L dI + RI dt
0
2 Determine the order, unknown function, and the independent variable in each of the following differential
equations:
10
3
(a)
(c)
8
- 5xy' = et + 1
d't
ds2
(a)
dt
+ st = s
ds
d²x
=
y = y² + 1
dy²
(c) 2x + 3x - 5x = 0
(b)
(d)
tÿ+t²y−(sint)√√y=t² −1
(b)
(a) y=x₂
5
Determine the order, unknown function, and the independent variable in each of the following
differential equations:
5 Is y(x) = 1 a solution of y" + 2y' + y = x?
y
(b) y=x8x²,
+ 7
dx
dy
(d) 17y(4) — 16(2) - 4.2y³ = 3 cos t
db
dp
4 Determine whether y(x) = 2e¯* + xe¯ is a solution of y" + 2y' + y = 0.
10
x² +1
6 Determine whether any of the functions (a) y₁ = sin 2x, (b) y₂(x) = x, or (c) y²3 (x) = sin 2x is a solution
to the initial-value problem y" + 4y = 0; y(0) = 0, y (0) = 1.
(c)
−1+1
7 Which of the following functions are solutions of the differential equation y' – 5y = 0?
(a) y = 5,
(b) y = 5x, (c) y=x³, (d) y=e³x,
(e) y=2e5x, (f) y = 5e²x
Which of the following functions are solutions of the differential equation y' – 3y = 6?
(a) y=-2, (b) y = 0, (c) y=e³x-2, (d) y=e²x-3, (e) y = 4e³x - 2
+ b² − b² = p
9 Which of the following functions are solutions of the differential equation
dy 2y + x²
dx
xy
y =
= √√x³ − x¹,
(d) y = (x8x4) ¹/4
Which of the following functions are solutions of the differential equation x − 4x + 4x = e
(a) x=e¹, (b) x=e²t (c) x = e²t + e¹, (d) x=te²t + e¹, (e) x = e²t + tet](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56514a45-1715-4000-bef0-87ece83531e6%2F4cff7515-00f9-496e-9f53-ffbfa445a684%2F3o37ri_processed.png&w=3840&q=75)
Transcribed Image Text:1 Find the explicit solution to the equation
L dI + RI dt
0
2 Determine the order, unknown function, and the independent variable in each of the following differential
equations:
10
3
(a)
(c)
8
- 5xy' = et + 1
d't
ds2
(a)
dt
+ st = s
ds
d²x
=
y = y² + 1
dy²
(c) 2x + 3x - 5x = 0
(b)
(d)
tÿ+t²y−(sint)√√y=t² −1
(b)
(a) y=x₂
5
Determine the order, unknown function, and the independent variable in each of the following
differential equations:
5 Is y(x) = 1 a solution of y" + 2y' + y = x?
y
(b) y=x8x²,
+ 7
dx
dy
(d) 17y(4) — 16(2) - 4.2y³ = 3 cos t
db
dp
4 Determine whether y(x) = 2e¯* + xe¯ is a solution of y" + 2y' + y = 0.
10
x² +1
6 Determine whether any of the functions (a) y₁ = sin 2x, (b) y₂(x) = x, or (c) y²3 (x) = sin 2x is a solution
to the initial-value problem y" + 4y = 0; y(0) = 0, y (0) = 1.
(c)
−1+1
7 Which of the following functions are solutions of the differential equation y' – 5y = 0?
(a) y = 5,
(b) y = 5x, (c) y=x³, (d) y=e³x,
(e) y=2e5x, (f) y = 5e²x
Which of the following functions are solutions of the differential equation y' – 3y = 6?
(a) y=-2, (b) y = 0, (c) y=e³x-2, (d) y=e²x-3, (e) y = 4e³x - 2
+ b² − b² = p
9 Which of the following functions are solutions of the differential equation
dy 2y + x²
dx
xy
y =
= √√x³ − x¹,
(d) y = (x8x4) ¹/4
Which of the following functions are solutions of the differential equation x − 4x + 4x = e
(a) x=e¹, (b) x=e²t (c) x = e²t + e¹, (d) x=te²t + e¹, (e) x = e²t + tet
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