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17. 18. ӘМ ду (A) у + 2ry² (B) 0 1/ам May (A) Зу (B) х) - ?х (B) - aN - ) Әх (C) 3y+6ху² (D) 1 + 2ry (C) (D) -3y 19. The integrating factor for the given differential equation is (A) (C) О (D) -

17. 18. ӘМ ду (A) у + 2ry² (B) 0 1/ам May (A) Зу (B) х) - ?х (B) - aN - ) Әх (C) 3y+6ху² (D) 1 + 2ry (C) (D) -3y 19. The integrating factor for the given differential equation is (A) (C) О (D) -

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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For the next five questions, consider the following differential equation: (y² + 2xy³) dr + (5y² - xy + y³ siny) dy = 0 Let M be the coefficient of dr and N be the coefficient of dy.
Transcribed Image Text:For the next five questions, consider the following differential equation: (y² + 2xy³) dr + (5y² - xy + y³ siny) dy = 0 Let M be the coefficient of dr and N be the coefficient of dy.
17. 18. ƏM ду (A) y + 2xy² (B) 0 (-81)=- ƏN (OM-ON 1 /ƏM May (A) 3y (B) 19. The integrating factor for the given differential equation is (A) y 21. Which of the following statements is(are) true? (B)-¹ 20. Determine which of the following set of functions is(are) linearly independent on (-∞0,00). (A) f₁(x)=1, f₂(x)=x²₁ f₁(x) = 4x - 3x² (B) fi(x)=5, f2(x) = cos²x, f(x) = sin² r (C) fi(x) = 1, f(x)=x-1, fs(x) = 1 +3 (D) f(x)=e, f2(x) = e², f₁(x) = €² (A) ye is a solution of the DE y" + y - 12y = 0. (B) y"-6y + 5y = -9 In 2x is a nonhomogeneous linear DE which can be solved by undetermined coefficients. (C) The roots of the auxiliary equation of the DE y" + 5y +6y=0 are distinct imaginary. (D) The roots of the auxiliary equation of the DE y+3y" - 4y= 0 are both real and distinct. (C) 3y+6ry2 (D) 1+2ry 22. Which of the following describes the nature of roots of the auxiliary equation corresponding to the DE 4) + 3y + 6y" +5y+3y=0? (A) m = - (C) (D) -3y (A) real repeated; imaginary distinct (B) real - distinct; imaginary - distinct (C) real - distinct; real-repeated; imaginary - distinct (D) imaginary repeated (B) m = - 23. What are the roots of the auxiliary equation corresponding to the DE y(4)+3y"+6y"+5y+3y=0 √√3. -1/2+1/3³, ± i, (C) (D) --- 1 √3. 2 = 2¹ un 23 3:2 (A) m = 1, 23 (B) m=1,3¹2 -1± √/²i 1+√2i 24. What are the roots of the auxiliary equation corresponding to the DE 6y" +11y" -/- 6y=0? (C) m = = 1/2+1/³₁,-1+√/²i 1 √3. (D) m=2" 2,1± √2i ± 2 3 3 2 (C) m = -1. 23 (D) m=32 25. Write the general solution for the homogeneous DE 6y" - y" - 11y' +6y=0. (A) y = ge+gel² + gele (C) y = ce+c₂e-t² + c₂e-1² (B) y=ce+c₂e-1² +₂e²² (D) y=ce+c₂e³² + get ² DD m
Transcribed Image Text:17. 18. ƏM ду (A) y + 2xy² (B) 0 (-81)=- ƏN (OM-ON 1 /ƏM May (A) 3y (B) 19. The integrating factor for the given differential equation is (A) y 21. Which of the following statements is(are) true? (B)-¹ 20. Determine which of the following set of functions is(are) linearly independent on (-∞0,00). (A) f₁(x)=1, f₂(x)=x²₁ f₁(x) = 4x - 3x² (B) fi(x)=5, f2(x) = cos²x, f(x) = sin² r (C) fi(x) = 1, f(x)=x-1, fs(x) = 1 +3 (D) f(x)=e, f2(x) = e², f₁(x) = €² (A) ye is a solution of the DE y" + y - 12y = 0. (B) y"-6y + 5y = -9 In 2x is a nonhomogeneous linear DE which can be solved by undetermined coefficients. (C) The roots of the auxiliary equation of the DE y" + 5y +6y=0 are distinct imaginary. (D) The roots of the auxiliary equation of the DE y+3y" - 4y= 0 are both real and distinct. (C) 3y+6ry2 (D) 1+2ry 22. Which of the following describes the nature of roots of the auxiliary equation corresponding to the DE 4) + 3y + 6y" +5y+3y=0? (A) m = - (C) (D) -3y (A) real repeated; imaginary distinct (B) real - distinct; imaginary - distinct (C) real - distinct; real-repeated; imaginary - distinct (D) imaginary repeated (B) m = - 23. What are the roots of the auxiliary equation corresponding to the DE y(4)+3y"+6y"+5y+3y=0 √√3. -1/2+1/3³, ± i, (C) (D) --- 1 √3. 2 = 2¹ un 23 3:2 (A) m = 1, 23 (B) m=1,3¹2 -1± √/²i 1+√2i 24. What are the roots of the auxiliary equation corresponding to the DE 6y" +11y" -/- 6y=0? (C) m = = 1/2+1/³₁,-1+√/²i 1 √3. (D) m=2" 2,1± √2i ± 2 3 3 2 (C) m = -1. 23 (D) m=32 25. Write the general solution for the homogeneous DE 6y" - y" - 11y' +6y=0. (A) y = ge+gel² + gele (C) y = ce+c₂e-t² + c₂e-1² (B) y=ce+c₂e-1² +₂e²² (D) y=ce+c₂e³² + get ² DD m
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