1 2 3 4 5 6 7 Which of the following is a second-order linear nonhomogenous ODE? A) sin(x)y" + y = 0 B) sin(x)y"+y+3=0 C) sin(x) (y)² + D) sin(x) 4 Find the general solution of y'+-y=4x ? A) y=x² + B) y=x² + C) y = x² + D). x Find the values for the constants a, b in which the ODE (axy-by²) dx-(x² + 4xy) dy = 0 is exact? A) a=3,b=-2 B) a=-3,b=-2 D) a=0,b=-2 C) a=3,b=-4 By using a suitable substitution, the Bernoulli ODE y'+ xy = y, becomes a linear ODE of the form: A) u'-4xu=-4 B) u'-3x = -3u C) u'+3xu=3 D) u'- 3xu = -3 Find the exact solution for x'y'-y=0, y(1)=1 A) y=e³ +e_B) y=e¹² C)y=e=² +6 D) y = e¹= By using a suitable substitution, the non-separable ODE xy'=x+y, is reduces to a separable ODE of the C) xu'+2u=0 D) u'=-x 17 B) u'=x Find the general solution of y"-3y=0 A)u' = A) y=q₁x+c₂e¹ C)y=+₂e³x y = 0 B) y=ce² +₂e²¹ D) y=c₁ +₂e d e value(s) fork in which the general solution of 3y"+y+ky=0 is of the form ce +exe^, c₂, are real constants) A) k = 12 B) k=0 C) k = 1 D) k = Find an ODE whose basis of the general solution the functions y, = sin 3x, y₂ = cos 3.x A) y"-9y=0 B) y"+9y=0 C) y"-3y=0 10 The integrating factor of the non-exact D.E. (ex+y+ye) dx + (xey-1) dy = 0 D) y"+3y=0 (a) e-> (b)-y 11 the general solution for the second order ODE y" + 11y' +24y = 0 (c) y³ a) y = C₁ ex +C₂ e³x 12 the integrating factor for the first order ODE y' = 3 + 2y is (b) e² (a) e² e-2x (d) e²x -8x (b) y = C₁ e +C₂ ex (c) e (c) y = C₁ ex +C₂ e³ (d) y =
1 2 3 4 5 6 7 Which of the following is a second-order linear nonhomogenous ODE? A) sin(x)y" + y = 0 B) sin(x)y"+y+3=0 C) sin(x) (y)² + D) sin(x) 4 Find the general solution of y'+-y=4x ? A) y=x² + B) y=x² + C) y = x² + D). x Find the values for the constants a, b in which the ODE (axy-by²) dx-(x² + 4xy) dy = 0 is exact? A) a=3,b=-2 B) a=-3,b=-2 D) a=0,b=-2 C) a=3,b=-4 By using a suitable substitution, the Bernoulli ODE y'+ xy = y, becomes a linear ODE of the form: A) u'-4xu=-4 B) u'-3x = -3u C) u'+3xu=3 D) u'- 3xu = -3 Find the exact solution for x'y'-y=0, y(1)=1 A) y=e³ +e_B) y=e¹² C)y=e=² +6 D) y = e¹= By using a suitable substitution, the non-separable ODE xy'=x+y, is reduces to a separable ODE of the C) xu'+2u=0 D) u'=-x 17 B) u'=x Find the general solution of y"-3y=0 A)u' = A) y=q₁x+c₂e¹ C)y=+₂e³x y = 0 B) y=ce² +₂e²¹ D) y=c₁ +₂e d e value(s) fork in which the general solution of 3y"+y+ky=0 is of the form ce +exe^, c₂, are real constants) A) k = 12 B) k=0 C) k = 1 D) k = Find an ODE whose basis of the general solution the functions y, = sin 3x, y₂ = cos 3.x A) y"-9y=0 B) y"+9y=0 C) y"-3y=0 10 The integrating factor of the non-exact D.E. (ex+y+ye) dx + (xey-1) dy = 0 D) y"+3y=0 (a) e-> (b)-y 11 the general solution for the second order ODE y" + 11y' +24y = 0 (c) y³ a) y = C₁ ex +C₂ e³x 12 the integrating factor for the first order ODE y' = 3 + 2y is (b) e² (a) e² e-2x (d) e²x -8x (b) y = C₁ e +C₂ ex (c) e (c) y = C₁ ex +C₂ e³ (d) y =
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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Transcribed Image Text:1
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Which of the following is a second-order linear nonhomogenous ODE?
A) sin(x)y" + y = 0 B) sin(x)y"+y+3=0 C) sin(x) (y)² + y = 0 D) sin(x)
4
Find the general solution of y'+-y=4x ? A) y=x² + B) y=x²+0) y = x² + D).
Find the values for the constants a, b in which the ODE (axy-by²) dx-(x² + 4xy) dy=0 is exact?
X
A) a = 3,b= -2
B) a=-3,b=-2
C) a=3,b=-4
D) a=0,b=-2
By using a suitable substitution, the Bernoulli ODE y'+ xy = y, becomes a linear ODE of the form:
A) u'-4xu=-4 B) u'-3x=-3u
C) u'+3xu=3
D) u'- 3xu = -3
Find the exact solution for x'y'-y=0, y(1)=1
A) y=e² +e B) y=e¹-² C)y=e=²+e_D)y=e¹
By using a suitable substitution, the non-separable ODE xy'=x+y, is reduces to a separable ODE of the
1
A)u'=-
B) u'=x
C) xu'+2u=0 D) u'=-x
Find the general solution of y"-3y'=0
A) y=q₁x+c₂₁e¹
C)y=+₂e³x
B) y=ce ¹ +ce²
D) y=c₁ +₂e
d
e value(s) fork in which the general solution of 3y"+y+ky=0 is of the form ce +exe^
c₂,2 are real constants}
A) k = 12
B) k=0
C) k = 1
D) k = =
Find an ODE whose basis of the general solution the functions y, = sin 3x, y₂ = cos 3x
A) y"-9y=0
B) y"+9y=0
C) y"-3y=0
10 The integrating factor of the non-exact D.E. (ex+y+ye) dx + (xey-1) dy = 0
D) y"+3y=0
(a) e->
(b)-y
(c) y ³
11 the general solution for the second order ODE y" + 11y' + 24y = 0
-8x
3x
a) y = C₁ ex+C₂ e³x
-8x
-3x
(b) y = C₁ e +C₂ e (c) y = C₁ e +C₂ e³¹ (d) y =
12 the integrating factor for the first order ODE y' = 3+2y is
(a) e²
(b) e²
e-2x
(d) e²x
(c) e
(d)
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