1. Determine the order and degree of the differential equation (A) order: 2, degree:4 (B) order: 4, degree:2 ² (1³)* + 4² (2³) ² - ¹ = 0. -22² (C) order: 2, degree:2 (D) order: 4, degree:4
1. Determine the order and degree of the differential equation (A) order: 2, degree:4 (B) order: 4, degree:2 ² (1³)* + 4² (2³) ² - ¹ = 0. -22² (C) order: 2, degree:2 (D) order: 4, degree:4
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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HELP ME PLEASE
![1. Determine the order and degree of the differential equation
(A) order: 2, degree:4
(B) order: 4, degree:2
(A)
(B)
(A)
2. The equation y = cr² is the one-parameter family of solutions of which of the following differential
equations?
dy
(B)
2y
I
y
dr 2x
dy
dx
dy
dr
= 3x-2y
ry+3r-y-3
ry-2r-4y+8
-2²² ()*+
(A) I only
(B) II only
5. The following DE are exact except
3. The following differential equations are variable separable except
(A) 2ry³ +e+ (3r²y² + sin y)y' =0
(B) 6ry³ +2y + (92³y² +8ry³)y=0
47 (21) ² -
dr²
+ 4x
(A) ) (³²-√²² + y²) dr-
(C) order: 2, degree:2
(D) order: 4, degree:4
(C)
dr-r²dy = 0
(D)
(B) (x+2y-1)dx = (x+2y-3)dy
dy
dr
-1=0.
dy
dr
(D)
4. Which of the following statement(s) is (are) true?
I. y = e-2/2 is a particular solution of 2y + y = 0
II. y = e² cos 3r is a particular solution of y" - 6y + 13y = 0
2y
I
(C) 2ydr = (²+2x+1)dy
dN
dt
y
2r
+N=
(A) The given DE is separable and exact.
(B) The given DE is separable and Bernoulli.
(C) The given DE is exact and has homogeneous coefficients.
(D) The given DE is linear and exact.
(C) both I and II
(D) neither I nor II
6. Which of the following is(are) true about the equation.
(A) The differential equation is variable separable.
(B) The differential equation is linear in y.
(C) The differential equation is exact.
(D) The differential equation is Bernoulli.
7. Which of the following statements is true about the DE, dy √9-9₂
dr
tan z
N
te²+2
(C) 2rydr + (2+x²)dy = 0
(D) (²+1)dr-zydy = 0
(D) tan
dy
dt + y²=ty??
8. Which of the following is(are) a differential equation(s) with homogeneous coefficients?
(C)
) ( y − √2² + y²) dx - zdy = 0
(dy -[(-)tan (+2] dr = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dd6233c-1070-4807-9af0-a9dc97ab8ebc%2F024d8083-ba1f-4867-8816-cbf5df12e6b4%2F6ts2vf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Determine the order and degree of the differential equation
(A) order: 2, degree:4
(B) order: 4, degree:2
(A)
(B)
(A)
2. The equation y = cr² is the one-parameter family of solutions of which of the following differential
equations?
dy
(B)
2y
I
y
dr 2x
dy
dx
dy
dr
= 3x-2y
ry+3r-y-3
ry-2r-4y+8
-2²² ()*+
(A) I only
(B) II only
5. The following DE are exact except
3. The following differential equations are variable separable except
(A) 2ry³ +e+ (3r²y² + sin y)y' =0
(B) 6ry³ +2y + (92³y² +8ry³)y=0
47 (21) ² -
dr²
+ 4x
(A) ) (³²-√²² + y²) dr-
(C) order: 2, degree:2
(D) order: 4, degree:4
(C)
dr-r²dy = 0
(D)
(B) (x+2y-1)dx = (x+2y-3)dy
dy
dr
-1=0.
dy
dr
(D)
4. Which of the following statement(s) is (are) true?
I. y = e-2/2 is a particular solution of 2y + y = 0
II. y = e² cos 3r is a particular solution of y" - 6y + 13y = 0
2y
I
(C) 2ydr = (²+2x+1)dy
dN
dt
y
2r
+N=
(A) The given DE is separable and exact.
(B) The given DE is separable and Bernoulli.
(C) The given DE is exact and has homogeneous coefficients.
(D) The given DE is linear and exact.
(C) both I and II
(D) neither I nor II
6. Which of the following is(are) true about the equation.
(A) The differential equation is variable separable.
(B) The differential equation is linear in y.
(C) The differential equation is exact.
(D) The differential equation is Bernoulli.
7. Which of the following statements is true about the DE, dy √9-9₂
dr
tan z
N
te²+2
(C) 2rydr + (2+x²)dy = 0
(D) (²+1)dr-zydy = 0
(D) tan
dy
dt + y²=ty??
8. Which of the following is(are) a differential equation(s) with homogeneous coefficients?
(C)
) ( y − √2² + y²) dx - zdy = 0
(dy -[(-)tan (+2] dr = 0
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