14. In the system of inear 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 (A) Unique solution (B) No solution 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+c=d₁ ax+by+cz=d₂ (C) Infinitely many solution (D) None of these 16. The partial differential equation of z=f(x+at)-g(x-at) is. (A) (C) a'z ar² =a² a'z ax² az Ə²= ar² ax² (B) 1.11 (A) xyz,-+-+- 2 / 20 (D) -0 ar 11 a'z a'z ar² ax² - 17. The first order partial differential equation by eliminat- ing the arbitary function from z=f(x²-y³) is (A) p+q=0 (C) ²p+x²q=0 (B) yp+xq=0 (D) 2y'p+3x'q=0 wwwww.pen wwwwwwww 18. The general solution of the partial differential equation x(y-2)p+y(2-x)q = ='(x-y) is 100% + (C)2 2 ential equation 4 (A) X(x) = ce) ² ce(). 21. If a(x, y)= X(x). Y(y) be the solution of the partial differ- du du +5 = 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: Herec and k are arbitrary constants] (B) X(x)= ce (D) X(x) = ce² 22. Which of the following second order partial differential equations is an elliptic equation? (C) X(x) = d'u d'u (A) 3- +4 ar² axdy 2²M ax² (B) 3- (D) (C) -3- -4- d'u d'u +4- dx² axdy d'u dy² +5 +7 au d'u du du +5 ахду ду ах ду d'u d'u d'u +2- drdy dy + dx² d'u dy² 29 du du dx dy 0, which is obtained by (B) (D) +4x- + = 6x³y du ax du du dx dy +5 = 7x² DYT -7y dy 6xy² a-b =0 23. The Fourier cosine series of the function f(x) = 0≤xslis (A) 1 (C) 0
14. In the system of inear 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 (A) Unique solution (B) No solution 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+c=d₁ ax+by+cz=d₂ (C) Infinitely many solution (D) None of these 16. The partial differential equation of z=f(x+at)-g(x-at) is. (A) (C) a'z ar² =a² a'z ax² az Ə²= ar² ax² (B) 1.11 (A) xyz,-+-+- 2 / 20 (D) -0 ar 11 a'z a'z ar² ax² - 17. The first order partial differential equation by eliminat- ing the arbitary function from z=f(x²-y³) is (A) p+q=0 (C) ²p+x²q=0 (B) yp+xq=0 (D) 2y'p+3x'q=0 wwwww.pen wwwwwwww 18. The general solution of the partial differential equation x(y-2)p+y(2-x)q = ='(x-y) is 100% + (C)2 2 ential equation 4 (A) X(x) = ce) ² ce(). 21. If a(x, y)= X(x). Y(y) be the solution of the partial differ- du du +5 = 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: Herec and k are arbitrary constants] (B) X(x)= ce (D) X(x) = ce² 22. Which of the following second order partial differential equations is an elliptic equation? (C) X(x) = d'u d'u (A) 3- +4 ar² axdy 2²M ax² (B) 3- (D) (C) -3- -4- d'u d'u +4- dx² axdy d'u dy² +5 +7 au d'u du du +5 ахду ду ах ду d'u d'u d'u +2- drdy dy + dx² d'u dy² 29 du du dx dy 0, which is obtained by (B) (D) +4x- + = 6x³y du ax du du dx dy +5 = 7x² DYT -7y dy 6xy² a-b =0 23. The Fourier cosine series of the function f(x) = 0≤xslis (A) 1 (C) 0
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
19, 21 through 24
![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
(B) O
(C) O
a'z
Əx²
(A) xyz,-+-
1
(C)
17. The first order partial differential equation by eliminat-
ing the arbitary function from z = fr-y) is
02 CREATIVE WRITERS-contract for X
(A) p+q=0
(B) yp+xq=0
(C) y²p+x²q=0
(D) 2y'p+3x'q=0
18. The general solution of the partial differential equation
x(y-2)p+y(2-x)q ==(x-y) is
1
(D) o E
1
+ + 1)-0
A
11 1
++ -+-
111
1- +
z x y Z
y zx
1
▬▬
(D)
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 an 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: Herec and k are arbitrary constants]
(B) 3
(D)
(C)
d'u
(A) 3: +4
dx
(C) -3
d is
2
(A)
A
22. Which of the following second order partial differential
equations is an elliptic equation?
d'u
axdy
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'u d'u d'u
+2.
dx² drdy dy²
+
(D) Z-WA Foy
d'u
Ju
+5
+4x-
axay dy
au dudu- 6x³y
+
ду ах ду
X
(B) X(x)= ce
(D) X(x) = ce) ²
(B)
(D)
24. The Fourier series of f(x) = e in the
(0, 2n) is
f(x) = + [a
al
du
ax
(B)
du du
-2 +5-
= 6.xy²
dx dy
23. The Fourier cosine series of the function fix) =
0≤xslis
(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%2Fdd497603-ad39-4dc5-9e12-644e3e72a543%2Fmyk8rtcf_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
(B) O
(C) O
a'z
Əx²
(A) xyz,-+-
1
(C)
17. The first order partial differential equation by eliminat-
ing the arbitary function from z = fr-y) is
02 CREATIVE WRITERS-contract for X
(A) p+q=0
(B) yp+xq=0
(C) y²p+x²q=0
(D) 2y'p+3x'q=0
18. The general solution of the partial differential equation
x(y-2)p+y(2-x)q ==(x-y) is
1
(D) o E
1
+ + 1)-0
A
11 1
++ -+-
111
1- +
z x y Z
y zx
1
▬▬
(D)
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 an 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: Herec and k are arbitrary constants]
(B) 3
(D)
(C)
d'u
(A) 3: +4
dx
(C) -3
d is
2
(A)
A
22. Which of the following second order partial differential
equations is an elliptic equation?
d'u
axdy
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'u d'u d'u
+2.
dx² drdy dy²
+
(D) Z-WA Foy
d'u
Ju
+5
+4x-
axay dy
au dudu- 6x³y
+
ду ах ду
X
(B) X(x)= ce
(D) X(x) = ce) ²
(B)
(D)
24. The Fourier series of f(x) = e in the
(0, 2n) is
f(x) = + [a
al
du
ax
(B)
du du
-2 +5-
= 6.xy²
dx dy
23. The Fourier cosine series of the function fix) =
0≤xslis
(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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