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2 + y = u B) sin(x)y+iy' +3=0 C)sin(x)(y') + y = 0 D) sin(x) Find the general solution of y'+ 12y=4x? A)y=x2+/2B)y=x+12cy=2x+12

2 + y = u B) sin(x)y+iy' +3=0 C)sin(x)(y') + y = 0 D) sin(x) Find the general solution of y'+ 12y=4x? A)y=x2+/2B)y=x+12cy=2x+12

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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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 + 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)
Transcribed Image Text: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 + 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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