(A) (C) 14. If the system of linear equations 2x + 3y + 4z= 1 5x-y+z=4 -3 (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 3x + ay-32= 3 has a unique solution, then the value of a + 4 (A) Unique solution (B) No solution (C) Infinitely many solution (D) None of these (A) 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. (C) ax+by+cz=d₁ ax+by+cz=d, 16. The partial differential equation of z=f(x+at) - g (x-at) is a'z a¹z Əx² (B) =a (C) 0¹2 dr ax (A) p+q=0 (C) y'p+xq=0 (D) B) JE (D) 11 1 (A) xyz, +-+-=0 x y 1 1 11 1 + + ** y² zx y 1 X y 1 (B) (D) drª 17. The first order partial differential equation by eliminat- ing the arbitary function from z=f(x³ -y²³) is dz dr 2 / 20 0 -4 18. The general solution of the partial differential equation x(y-z) p+y³(2-x)q=z'(x-y) is 11 1 z³x² y² 22 + 11 1 <=0 əz 0 191 dx (B) yp+xq=0 (D) 2y³p+ 3x³q=0 a²z dr² 100% (A) r²+²=(x²-y) (B) x²¹+z² = (x² - z²¹) (C) x²-y²=(−z²³) (D) y²-2²= (x²-yª² − z²) 20. The solution of (p-q)(z-xp-y q) = 1 is (A) z= ax-by+ (B) z-ax-by + (C) z = ax + by a-b 21. Ifu(x, y)= X(x). Y(y) be the solution of the partial differ- du du (A) X(x) = cek) ² (C) X(x) = c(i) H ential equation 4- +5 = 0, which is obtained by ax 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) 22. Which of the following second order partial differential equations is an elliptic equation? 1 a+b d'u d'u d'u du du (A) 3 +4 -5- +7 dxdy dy Әх ду dx² a²u dx² (A) d'u (C) -3 +4 drª axdy dy² 0 ≤x≤lis (A) 1 (C) 0 a 99 is f(x) = + (D) z= ax+by+ (B) X(x)= ce (D) X(x) = ce)² 4 d'u d'u du du +5 + = 6x²y axdy ду² Әх ду +5 d'u d'u au du du +2+ 2 +5 dxdy dy dx dy + Əx² d'u d'u du +4x -7y ax 24. The Fourier series of f(x) = e in the (0, 2n) is 1 23. The Fourier cosine series of the function f(x) = 2 Σa, cos mx+ = (B) (D) = 7x² (B) du dy 6.xy² =0 19 42 interval +Σb, sin nx, then the value of
(A) (C) 14. If the system of linear equations 2x + 3y + 4z= 1 5x-y+z=4 -3 (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 3x + ay-32= 3 has a unique solution, then the value of a + 4 (A) Unique solution (B) No solution (C) Infinitely many solution (D) None of these (A) 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. (C) ax+by+cz=d₁ ax+by+cz=d, 16. The partial differential equation of z=f(x+at) - g (x-at) is a'z a¹z Əx² (B) =a (C) 0¹2 dr ax (A) p+q=0 (C) y'p+xq=0 (D) B) JE (D) 11 1 (A) xyz, +-+-=0 x y 1 1 11 1 + + ** y² zx y 1 X y 1 (B) (D) drª 17. The first order partial differential equation by eliminat- ing the arbitary function from z=f(x³ -y²³) is dz dr 2 / 20 0 -4 18. The general solution of the partial differential equation x(y-z) p+y³(2-x)q=z'(x-y) is 11 1 z³x² y² 22 + 11 1 <=0 əz 0 191 dx (B) yp+xq=0 (D) 2y³p+ 3x³q=0 a²z dr² 100% (A) r²+²=(x²-y) (B) x²¹+z² = (x² - z²¹) (C) x²-y²=(−z²³) (D) y²-2²= (x²-yª² − z²) 20. The solution of (p-q)(z-xp-y q) = 1 is (A) z= ax-by+ (B) z-ax-by + (C) z = ax + by a-b 21. Ifu(x, y)= X(x). Y(y) be the solution of the partial differ- du du (A) X(x) = cek) ² (C) X(x) = c(i) H ential equation 4- +5 = 0, which is obtained by ax 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) 22. Which of the following second order partial differential equations is an elliptic equation? 1 a+b d'u d'u d'u du du (A) 3 +4 -5- +7 dxdy dy Әх ду dx² a²u dx² (A) d'u (C) -3 +4 drª axdy dy² 0 ≤x≤lis (A) 1 (C) 0 a 99 is f(x) = + (D) z= ax+by+ (B) X(x)= ce (D) X(x) = ce)² 4 d'u d'u du du +5 + = 6x²y axdy ду² Әх ду +5 d'u d'u au du du +2+ 2 +5 dxdy dy dx dy + Əx² d'u d'u du +4x -7y ax 24. The Fourier series of f(x) = e in the (0, 2n) is 1 23. The Fourier cosine series of the function f(x) = 2 Σa, cos mx+ = (B) (D) = 7x² (B) du dy 6.xy² =0 19 42 interval +Σb, sin nx, then the value of
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 19 through 24
![Inbox (13,580) - thomaskielbasins X
).pdf
(A)
Ô
NE
14. If the system of linear equations
2x + 3y + 4z= 1
5x-y+z=4
mm
3
D--
(C) Infinitely many solution
(D) None of these
(C)
16. The partial differential equation of
z=f(x+at)- g (x-at) is
dºz
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
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
(A) Unique solution
(B) No solution
ar
d²z d²z
dr du
=a
(A) p+q=0
(C) yp+rq=0
(B) O
e
1
1
•
(A) xyz,-+-+-=0
x y
4
2
(C) --
+
17. The first order partial differential equation by eliminat-
ing the arbitary function from z = f(x²³ -²¹) is
(B) yp + xq=0
(D) 2y p+ 3x³q=0
1
02 CREATIVE WRITERS-contract fe X
X y
18. The general solution of the partial differential equation
x(y-2) p+y(2-x)q = ='(x - y) is
2
1 1 1 1
+
Z x
B)
2
1 1 1
(D)
4
1
(B)
(D)
-+-+
X
2 / 20
+/+) = 0.
0
0
I
Y
70
=0
at dx
əz Əºz
+
di² ax²
0
-a
100%
+
(A) r²¹+y² = (x −y)
(B) x²+z=(x² – z²)
(C) x²-y²=(²– zª²)
(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) = ce(i)
21. Ifu(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: Herec 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfe4191b-d77f-491e-bfbe-133f2efb412f%2Fadc48c6b-ff20-45c7-8db2-a7256d3a7c10%2Fqgpvhvs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Inbox (13,580) - thomaskielbasins X
).pdf
(A)
Ô
NE
14. If the system of linear equations
2x + 3y + 4z= 1
5x-y+z=4
mm
3
D--
(C) Infinitely many solution
(D) None of these
(C)
16. The partial differential equation of
z=f(x+at)- g (x-at) is
dºz
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
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
(A) Unique solution
(B) No solution
ar
d²z d²z
dr du
=a
(A) p+q=0
(C) yp+rq=0
(B) O
e
1
1
•
(A) xyz,-+-+-=0
x y
4
2
(C) --
+
17. The first order partial differential equation by eliminat-
ing the arbitary function from z = f(x²³ -²¹) is
(B) yp + xq=0
(D) 2y p+ 3x³q=0
1
02 CREATIVE WRITERS-contract fe X
X y
18. The general solution of the partial differential equation
x(y-2) p+y(2-x)q = ='(x - y) is
2
1 1 1 1
+
Z x
B)
2
1 1 1
(D)
4
1
(B)
(D)
-+-+
X
2 / 20
+/+) = 0.
0
0
I
Y
70
=0
at dx
əz Əºz
+
di² ax²
0
-a
100%
+
(A) r²¹+y² = (x −y)
(B) x²+z=(x² – z²)
(C) x²-y²=(²– zª²)
(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) = ce(i)
21. Ifu(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: Herec 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
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