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11 the general solution for the second order ODE y" + 11y' + 24y = 0 -8x a) y = C₁ ex+C₂ e³x (b) y = C₁ ex+C₂ e ³x 12 the integrating fanten Co ODD (c) y = C₁ ex+C₂ e³x (d) y (d) y = C₁

11 the general solution for the second order ODE y" + 11y' + 24y = 0 -8x a) y = C₁ ex+C₂ e³x (b) y = C₁ ex+C₂ e ³x 12 the integrating fanten Co ODD (c) y = C₁ ex+C₂ e³x (d) y (d) y = C₁

Advanced Engineering Mathematics
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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2 9 3 4 5 6 8 7 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
Transcribed Image Text:2 9 3 4 5 6 8 7 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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