14. If the system of inear equations 2x+3y + 4z=1 5x-y+z=4 3x + ay-32-3 has a unique solution, then the value of a + 4. (A) must be equal to 0, (B) should not be equal to 0 (C) can be any real number, can be any rational number h (D) 15. If a
14. If the system of inear equations 2x+3y + 4z=1 5x-y+z=4 3x + ay-32-3 has a unique solution, then the value of a + 4. (A) must be equal to 0, (B) should not be equal to 0 (C) can be any real number, can be any rational number h (D) 15. If a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please answer all questions just with letter answer no step by step
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14. In the system of inear equations
2x+3y + 4z = 1
5x-y+z=4
3x + ay-32-3
has a unique solution, then the value of a + 4
(A) must be equal to 0,
(B) should not be equal to 0
(C) can be any real number,
(D) can be any rational number
(A) Unique solution
(B) No solution
(C) Infinitely many solution
(D) None of these
15. If a, b, c, d,, a, b, c, and d, are any non zero real
numbers, then which of the following types of solution
is NOT possible for the system of linear equations.
ax+by+cz=d₁
ax+by+cz=d₂
16. The partial differential equation of
z=f(x+at)-g (x-at) is_______
d²z
(B)
(A)
a²z a²z
=
di² ax²
a²
(A) p+q=0
(C) y²p+x²q=0
a'z
Əx²
(B) O
(C) O
(A) xyz,-+
(C)
17. The first order partial differential equation by eliminat-
ing the arbitary function from z=f(x-³) is
1
02 CREATIVE WRITERS-contract for X
1
(D) o E
A
18. The general solution of the partial differential equation
x(y-2)p+y(2-x)q=z³(x-y) is
1
+ + 1)-0
++
111
1- +
11 1
-+-
z x y Z
y zx
1
▬▬
(D)
(B) yp+xq=0
(D) 2y'p+3x'q=0
2 / 20
dz
dz
=a
dr dx
a²z a²z
dr² ax²
意)。
DUET
<=0
²
mt
-0
11 1
y²z²x y
19. The solution of the partial differential equation
xy²z²p+xyz²q = x²y³z is
-
++)-0
Q Search
100%
+1
(C) 2 av Toy
Untitled (4)
(A) X(x)= ce x²
(C) X(x) = cel(²)
се
a-b
21. If (x,y)= X(x). Y(y) be the solution of the partial differ-
ential equation 4:
du ди
+5. = 0, which is obtained by
dx dy
solving it by the method of separation of variables, then
X(x) (the function of x only in u(x, y)) is
[Note: Here e and k are arbitrary constants]
(B) 3
(D)
d'u
(A) 3: +4
dx
(C) -3
(C)
22. Which of the following second order partial differential
equations is an elliptic equation?
d'u
axdy
d is
2
(A)
A
2²
dx²
d'u
4
d'u
axdy
ex-1
4x
e-l
2K
+4
+5.
d'u du du
15 +7
dy² dx dy
(D) 2-W Foy
d'u
Ju
+5
+4x-
axay dy
X
(B) X(x)= ce
(D) X(x)= ce) ²
du du du- 6x³y
+
ду ах ду
(B)
(D)
24. The Fourier series of f(x) = e in the
(0, 2n) is
f(x) = + [a
al
du
ax
d'u d'u d'u
du
+2.
du
dx²
-2 +5-
= 6.xy²
dxdy dy dx dy
+
(B)
23. The Fourier cosine series of the function fix) =
0≤x≤lis
(A) 1
(C) 0
(D)
+
(+)
= 7x²
e²-1
2x
e²-1
4x
du
7y=0
dy
1a
42
a, cos nx+b, sin nx, then the value of
interval](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfe4191b-d77f-491e-bfbe-133f2efb412f%2F9fbd5237-ccd0-4239-b243-c4ff97dc51ba%2Fcdv5mp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:M Inbox (13,580) - thomaskielbasin X
%20(1).pdf
14. In the system of inear equations
2x+3y + 4z = 1
5x-y+z=4
3x + ay-32-3
has a unique solution, then the value of a + 4
(A) must be equal to 0,
(B) should not be equal to 0
(C) can be any real number,
(D) can be any rational number
(A) Unique solution
(B) No solution
(C) Infinitely many solution
(D) None of these
15. If a, b, c, d,, a, b, c, and d, are any non zero real
numbers, then which of the following types of solution
is NOT possible for the system of linear equations.
ax+by+cz=d₁
ax+by+cz=d₂
16. The partial differential equation of
z=f(x+at)-g (x-at) is_______
d²z
(B)
(A)
a²z a²z
=
di² ax²
a²
(A) p+q=0
(C) y²p+x²q=0
a'z
Əx²
(B) O
(C) O
(A) xyz,-+
(C)
17. The first order partial differential equation by eliminat-
ing the arbitary function from z=f(x-³) is
1
02 CREATIVE WRITERS-contract for X
1
(D) o E
A
18. The general solution of the partial differential equation
x(y-2)p+y(2-x)q=z³(x-y) is
1
+ + 1)-0
++
111
1- +
11 1
-+-
z x y Z
y zx
1
▬▬
(D)
(B) yp+xq=0
(D) 2y'p+3x'q=0
2 / 20
dz
dz
=a
dr dx
a²z a²z
dr² ax²
意)。
DUET
<=0
²
mt
-0
11 1
y²z²x y
19. The solution of the partial differential equation
xy²z²p+xyz²q = x²y³z is
-
++)-0
Q Search
100%
+1
(C) 2 av Toy
Untitled (4)
(A) X(x)= ce x²
(C) X(x) = cel(²)
се
a-b
21. If (x,y)= X(x). Y(y) be the solution of the partial differ-
ential equation 4:
du ди
+5. = 0, which is obtained by
dx dy
solving it by the method of separation of variables, then
X(x) (the function of x only in u(x, y)) is
[Note: Here e and k are arbitrary constants]
(B) 3
(D)
d'u
(A) 3: +4
dx
(C) -3
(C)
22. Which of the following second order partial differential
equations is an elliptic equation?
d'u
axdy
d is
2
(A)
A
2²
dx²
d'u
4
d'u
axdy
ex-1
4x
e-l
2K
+4
+5.
d'u du du
15 +7
dy² dx dy
(D) 2-W Foy
d'u
Ju
+5
+4x-
axay dy
X
(B) X(x)= ce
(D) X(x)= ce) ²
du du du- 6x³y
+
ду ах ду
(B)
(D)
24. The Fourier series of f(x) = e in the
(0, 2n) is
f(x) = + [a
al
du
ax
d'u d'u d'u
du
+2.
du
dx²
-2 +5-
= 6.xy²
dxdy dy dx dy
+
(B)
23. The Fourier cosine series of the function fix) =
0≤x≤lis
(A) 1
(C) 0
(D)
+
(+)
= 7x²
e²-1
2x
e²-1
4x
du
7y=0
dy
1a
42
a, cos nx+b, sin nx, then the value of
interval
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Follow-up Question
I need 15 through 24 answered
![Inbox (13,580) - thomaskielbasins X
).pdf
(A)
Ô
NE
(A) Unique solution
(B) No solution
mm
3
D--
(C) Infinitely many solution
(D) None of these
(C)
14. If the system of linear equations
2x + 3y+4z=1
5x-y+z=4
3x + ay -3z = 3
has a unique solution, then the value of a + 4
(A) must be equal to 0,
(B) should not be equal to 0
(C) can be any real number,
(D) can be any rational number
16. The partial differential equation of
z=f(x+at) - g (x-at) is
dºz
15. If a, b, c, d,, a, b, c, and d, are any non zero real
numbers, then which of the following types of solution
is NOT possible for the system of linear equations.
ax+by+cz=d₁
+by+cz =d₂
ar
d²z d²z
dr du
=a
(A) p+q=0
(C) yp+rq=0
(B) O
e
1
1
(A) xyz,-+-+-=0
y
•
4
2
(C) --
+
17. The first order partial differential equation by eliminat-
ing the arbitary function from z=f(x² - y²¹) is
x
1
X y
18. The general solution of the partial differential equation
x(y-2) p+y³(2-x)q = ='(x - y) is
1 1 1
+
2
02 CREATIVE WRITERS-contract fe X
Z x
2
1 1 1
B)
(D)
X
4
1
(B)
(D)
-+-+
2 / 20
0
0
1 + 1) = 0.
Y
I
70
at dx
a²z Əºz
+
di dx²
(B) yp+xq=0
(D) 2y'p + 3x³q=0
=0
0
-a
100%
+
(A) r²¹+ y²= (r² =y')
(B) x²+z=(r² – z²)
(C) x²-y²=(− z²³)
(D) -2=(x−y² − z³)
20. The solution of (p-q) (z-xp-y q) = 1 is
(B) z= axby
Untitled (4)
(A) z= ax by +
(C) z= ax + by
(A) X(x)=ce²
(C) X(x) = c(i)
21. If u(x, y) = X(x). Y(y) be the solution of the partial differ-
du du
ential equation 4 +5. = 0, which is obtained by
əx dy
(C) -3
(D)
solving it by the method of separation of variables, then
X(x) (the function of x only in u(x, y)) is
[Note: Here c and k are arbitrary constants]
a²u d'u
(B) 3- -4. +5
dr² əxəy dy²
(A)
1
a+b
22. Which of the following second order partial differential
equations is an elliptic equation?
d'u d'u d'u du du
(A) 3- +4
5 +7
dr² dxdy
dx dy
d'u d'u
+4-
Əxəy
d'u
f(x) = +
+2
0≤x≤lis
(A) 1
(C) 0
+5
(D) z= ax + by +
d'u du
(B) X(x) = ce
(D) X(x) = ce
dx
au
du
+
Әхду ду dx
(B)
(D)
(B)
+
4x-
du
ax
du
ди
+5.
24. The Fourier series of f(x) = e in the
(0, 2n) is
+
= 6x²y
du
23. The Fourier cosine series of the function f(x) =
11/10
A
= 6.xy²
a-b
19
42
0
interval
Σα a, cos nx+b, sin nex, then the value of
+Σ
N](https://content.bartleby.com/qna-images/question/dfe4191b-d77f-491e-bfbe-133f2efb412f/d224056c-56f6-4299-b266-1fa92cd9c334/no9gsf_processed.jpeg)
Transcribed Image Text:Inbox (13,580) - thomaskielbasins X
).pdf
(A)
Ô
NE
(A) Unique solution
(B) No solution
mm
3
D--
(C) Infinitely many solution
(D) None of these
(C)
14. If the system of linear equations
2x + 3y+4z=1
5x-y+z=4
3x + ay -3z = 3
has a unique solution, then the value of a + 4
(A) must be equal to 0,
(B) should not be equal to 0
(C) can be any real number,
(D) can be any rational number
16. The partial differential equation of
z=f(x+at) - g (x-at) is
dºz
15. If a, b, c, d,, a, b, c, and d, are any non zero real
numbers, then which of the following types of solution
is NOT possible for the system of linear equations.
ax+by+cz=d₁
+by+cz =d₂
ar
d²z d²z
dr du
=a
(A) p+q=0
(C) yp+rq=0
(B) O
e
1
1
(A) xyz,-+-+-=0
y
•
4
2
(C) --
+
17. The first order partial differential equation by eliminat-
ing the arbitary function from z=f(x² - y²¹) is
x
1
X y
18. The general solution of the partial differential equation
x(y-2) p+y³(2-x)q = ='(x - y) is
1 1 1
+
2
02 CREATIVE WRITERS-contract fe X
Z x
2
1 1 1
B)
(D)
X
4
1
(B)
(D)
-+-+
2 / 20
0
0
1 + 1) = 0.
Y
I
70
at dx
a²z Əºz
+
di dx²
(B) yp+xq=0
(D) 2y'p + 3x³q=0
=0
0
-a
100%
+
(A) r²¹+ y²= (r² =y')
(B) x²+z=(r² – z²)
(C) x²-y²=(− z²³)
(D) -2=(x−y² − z³)
20. The solution of (p-q) (z-xp-y q) = 1 is
(B) z= axby
Untitled (4)
(A) z= ax by +
(C) z= ax + by
(A) X(x)=ce²
(C) X(x) = c(i)
21. If u(x, y) = X(x). Y(y) be the solution of the partial differ-
du du
ential equation 4 +5. = 0, which is obtained by
əx dy
(C) -3
(D)
solving it by the method of separation of variables, then
X(x) (the function of x only in u(x, y)) is
[Note: Here c and k are arbitrary constants]
a²u d'u
(B) 3- -4. +5
dr² əxəy dy²
(A)
1
a+b
22. Which of the following second order partial differential
equations is an elliptic equation?
d'u d'u d'u du du
(A) 3- +4
5 +7
dr² dxdy
dx dy
d'u d'u
+4-
Əxəy
d'u
f(x) = +
+2
0≤x≤lis
(A) 1
(C) 0
+5
(D) z= ax + by +
d'u du
(B) X(x) = ce
(D) X(x) = ce
dx
au
du
+
Әхду ду dx
(B)
(D)
(B)
+
4x-
du
ax
du
ди
+5.
24. The Fourier series of f(x) = e in the
(0, 2n) is
+
= 6x²y
du
23. The Fourier cosine series of the function f(x) =
11/10
A
= 6.xy²
a-b
19
42
0
interval
Σα a, cos nx+b, sin nex, then the value of
+Σ
N
Solution
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