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1) Determine the order and degree of the differential equation 3r a) Fourth order, first degree b) First order, third degree a) complementary solution b) particular solution 2) A solution of a differential equation free from arbitrary constants but cannot be obtained from the general solution whatever values are assigned to the arbitrary constants is called a 3) Classify the Differential equation cos z dy dr a) Separable but not Linear b) Linear but not Separable a) (x+1)y" -ry+y=0 b) (x-1)y" + xy + y = 0 a) (x² + y²)dr + 2xydy = 0 b) (r-y)dr + 2xydy=0 4) How many times do you need to differentiate y = 4a cos(2x - 3b) to obtain the corresponding differential equation? a) 2 b) 1 c) 3 5) What is the differential equation of the curve whose general solution is y= C₁+C₂². c) (x-1)y" - xy + y = 0 d) (x+1)y" + xy + y = 0 dy 8) The Bernoulli's equation z dr dz 2 2 a) = + ==== + xy = 6) Which of the following is the differential equation of the family of circles that passes through the origin and whose center is located at the x axis? +y= dz +5x² c) First order, fifth degree d) Second order, first degree 3 dy e) singular solution d) trivial solution 7) What value of N(x, y) will make the differential equation (3r2y + 4r2)dr + N(x,y)dy = 0 exact? a) x³ + ey b) ² +rev c) x³ + ev d) ³ +rev 1 can be reduced to which linear differential equation? y² 1 3 c) Separable and linear d) Homogeneous d) 4 c) (x²-y)dx + 2xy²dy = 0 d) (x² - y²)dx + 2xydy = 0 c) dz 1 dz I d) dz dr Т 2 2= 2 I

1) Determine the order and degree of the differential equation 3r a) Fourth order, first degree b) First order, third degree a) complementary solution b) particular solution 2) A solution of a differential equation free from arbitrary constants but cannot be obtained from the general solution whatever values are assigned to the arbitrary constants is called a 3) Classify the Differential equation cos z dy dr a) Separable but not Linear b) Linear but not Separable a) (x+1)y" -ry+y=0 b) (x-1)y" + xy + y = 0 a) (x² + y²)dr + 2xydy = 0 b) (r-y)dr + 2xydy=0 4) How many times do you need to differentiate y = 4a cos(2x - 3b) to obtain the corresponding differential equation? a) 2 b) 1 c) 3 5) What is the differential equation of the curve whose general solution is y= C₁+C₂². c) (x-1)y" - xy + y = 0 d) (x+1)y" + xy + y = 0 dy 8) The Bernoulli's equation z dr dz 2 2 a) = + ==== + xy = 6) Which of the following is the differential equation of the family of circles that passes through the origin and whose center is located at the x axis? +y= dz +5x² c) First order, fifth degree d) Second order, first degree 3 dy e) singular solution d) trivial solution 7) What value of N(x, y) will make the differential equation (3r2y + 4r2)dr + N(x,y)dy = 0 exact? a) x³ + ey b) ² +rev c) x³ + ev d) ³ +rev 1 can be reduced to which linear differential equation? y² 1 3 c) Separable and linear d) Homogeneous d) 4 c) (x²-y)dx + 2xy²dy = 0 d) (x² - y²)dx + 2xydy = 0 c) dz 1 dz I d) dz dr Т 2 2= 2 I

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) Determine the order and degree of the differential equation 3r d'y dz a) Fourth order, first degree. b) First order, third degree 2) A solution of a differential equation free from arbitrary constants but cannot be obtained from the general solution whatever values are assigned to the arbitrary constants is called a a) complementary solution b) particular solution 3) Classify the Differential equation cos z- dy dr a) Separable but not Linear b) Linear but not Separable a) (x² + y²)dr + 2xydy=0 b) (r-y)dx + 2xydy = 0 a) + xy= 4) How many times do you need to differentiate y = 4a cos(2x - 3b) to obtain the corresponding differential equation? a) 2 b) 1 c) 3 5) What is the differential equation of the curve whose general solution is y = C₁+C₂². a) (x+1)y" - ry+y=0 b) (x-1)y" + xy + y = 0 c) (x-1)y" - xy + y = 0 d) (x+1)y" + xy + y = 0 dz 2 +-2=- 2 dr 9) Solve: (x+y)dy - (x-y)dx=0 a) x² + y² = C 2 6) Which of the following is the differential equation of the family of circles that passes through the origin and whose center is located at the x axis? b) U H dz da c) First order, fifth degree d) Second order, first degree +5x² ² (1²) ²-2²-0 7) What value of N(x, y) will make the differential equation (3r2y + 4r2)dr + N(x,y)dy = 0 exact? a) x³ + ey b) x² +rev c) x³ + ev d) x³ + rev 1 y² +12= e) singular solution d) trivial solution dy 8) The Bernoulli's equation z +y= can be reduced to which linear differential equation? dz x c) Separable and linear d) Homogeneous c) (x²-y)dx + 2xy²dy = 0 d) (x² - y²)dx + 2xydy = 0 c) dz da d) 4 1 -N11 Т 1 x d) b) x² + 2xy + y² = C c) ² - 2xy + y² = C 10) Determine the integrating factor of the differential equation (y tan(z) - e²)dx + dy = 0 a) ecos(z) b) - cos(x) c) esin(z) dz dz 2 I 2 d) 2² - 2xy-y²= C d) - sin(x)
Transcribed Image Text:1) Determine the order and degree of the differential equation 3r d'y dz a) Fourth order, first degree. b) First order, third degree 2) A solution of a differential equation free from arbitrary constants but cannot be obtained from the general solution whatever values are assigned to the arbitrary constants is called a a) complementary solution b) particular solution 3) Classify the Differential equation cos z- dy dr a) Separable but not Linear b) Linear but not Separable a) (x² + y²)dr + 2xydy=0 b) (r-y)dx + 2xydy = 0 a) + xy= 4) How many times do you need to differentiate y = 4a cos(2x - 3b) to obtain the corresponding differential equation? a) 2 b) 1 c) 3 5) What is the differential equation of the curve whose general solution is y = C₁+C₂². a) (x+1)y" - ry+y=0 b) (x-1)y" + xy + y = 0 c) (x-1)y" - xy + y = 0 d) (x+1)y" + xy + y = 0 dz 2 +-2=- 2 dr 9) Solve: (x+y)dy - (x-y)dx=0 a) x² + y² = C 2 6) Which of the following is the differential equation of the family of circles that passes through the origin and whose center is located at the x axis? b) U H dz da c) First order, fifth degree d) Second order, first degree +5x² ² (1²) ²-2²-0 7) What value of N(x, y) will make the differential equation (3r2y + 4r2)dr + N(x,y)dy = 0 exact? a) x³ + ey b) x² +rev c) x³ + ev d) x³ + rev 1 y² +12= e) singular solution d) trivial solution dy 8) The Bernoulli's equation z +y= can be reduced to which linear differential equation? dz x c) Separable and linear d) Homogeneous c) (x²-y)dx + 2xy²dy = 0 d) (x² - y²)dx + 2xydy = 0 c) dz da d) 4 1 -N11 Т 1 x d) b) x² + 2xy + y² = C c) ² - 2xy + y² = C 10) Determine the integrating factor of the differential equation (y tan(z) - e²)dx + dy = 0 a) ecos(z) b) - cos(x) c) esin(z) dz dz 2 I 2 d) 2² - 2xy-y²= C d) - sin(x)
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