Q 12 please
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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Q 12 please
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Which of the following is a second-order linear nonhomogenous ODE?
C) sin(x) (y)² + y = 0 D) sin(x)y"y+
C) y = ²³ x² + D) y = ²x².
A) sin(x)y" + y = 0
B) sin(x)y" +
y + 3 = 0
2
3
A) y=e*² +e B) y=e¹² C)y=e³² +e_D) y=e¹
By using a suitable substitution, the non-separable ODE xy' = x³ + y, is reduces to a separable ODE of the form:
A)u' = = = =
1
B) u'=x
C) xu'+2u=0
D) u'= -x
Find the general solution of y"-3y'=0
A) y =q₁x+c₂e³
C) y = ₁+c₂e³x
D) y=q₁ +c₂e³x
Find the value(s) fork in which the general solution of 3y"+y+ky=0 is of the form c,e¹ + ₂x²,
{c₁, c₂, are real constants}
A) k = 12
B) k=0
C) k = 1
D) k = /2
1
12.
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
D) y"+3y=0
10 The integrating factor of the non-exact D.E. (ex+y+yey) dx + (xey-1) dy = 0
(a) e-y
4
Find the general solution of y'++y = 4x ?
B) y=x² +
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
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 = x² +
C
-2x
B) y=ce²+c₂e²
(b)-y
11 the general solution for the second order ODE y" + 11y' + 24y = 0
(c) y ³
a) y = C₁ ex+C₂ e³x
(b) y = C₁ ex+C₂ e ³x
-8x
12 the integrating factor for the first order ODE y' = 3 + 2y is
(a) e²
(b) e2
(c) e 2x
(d) e²x
(d) y-³
(c) y = C₁ e³x +C₂ e³x (d) y = C₁ e
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