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d'y Determine the order and degree of the differential equation 3r- a) Fourth order, first degree b) First order, third degree ² (1²) ²-²²-0 +5x² c) First order, fifth degree d) Second order, first degree

d'y Determine the order and degree of the differential equation 3r- a) Fourth order, first degree b) First order, third degree ² (1²) ²-²²-0 +5x² c) First order, fifth degree d) Second order, first degree

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 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) (r +1)y" - ry+y=0 b) (-1)y" + xy' + y =0 a) (x² + y²)dr + 2xydy = 0 b) (-y)dz +2rydy = 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. c) (-1)y" - xy +y=0 d) (x+1)y" + xy + y =0 2 U H 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? dz da b) +5x² ² (dz)²-²²-0 c) First order, fifth degree d) Second order, first degree c) singular solution d) trivial solution 7) What value of N(x, y) will make the differential equation (3r2y + 4x2)dr + N(x,y)dy = 0 exact? a) ³ + ey b) x² + xev c) ³ + ev d) x³ +rev 1 y² +12= c) Separable and linear d) Homogeneous dy 8) The Bernoulli's equation z +y= can be reduced to which linear differential equation? dr x c) (x²-y)dx+ 2xy²dy = 0 d) (x²- y²)dz + 2xydy = 0 dz 2 +-2=- 2 dr 9) Solve: (x+y)dy - (x - y)dx=0 a) x² + y² =C b) x² + 2xy + y² = C c) ² - 2xy + y² = C 10) Deteriniue the integrating factor of the differential equation (y tan(z)-e)dx + dy = 0 a) ecos(x) b) - cos(x) c) esin(z) d) 4 c) dz 1 da 1 x -N11 Т d) 2 dz dr T 2 d) z² - 2xy-y²=C d) - sin(x)
Transcribed Image Text:1) Determine the order and degree of the differential equation 3r 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) (r +1)y" - ry+y=0 b) (-1)y" + xy' + y =0 a) (x² + y²)dr + 2xydy = 0 b) (-y)dz +2rydy = 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. c) (-1)y" - xy +y=0 d) (x+1)y" + xy + y =0 2 U H 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? dz da b) +5x² ² (dz)²-²²-0 c) First order, fifth degree d) Second order, first degree c) singular solution d) trivial solution 7) What value of N(x, y) will make the differential equation (3r2y + 4x2)dr + N(x,y)dy = 0 exact? a) ³ + ey b) x² + xev c) ³ + ev d) x³ +rev 1 y² +12= c) Separable and linear d) Homogeneous dy 8) The Bernoulli's equation z +y= can be reduced to which linear differential equation? dr x c) (x²-y)dx+ 2xy²dy = 0 d) (x²- y²)dz + 2xydy = 0 dz 2 +-2=- 2 dr 9) Solve: (x+y)dy - (x - y)dx=0 a) x² + y² =C b) x² + 2xy + y² = C c) ² - 2xy + y² = C 10) Deteriniue the integrating factor of the differential equation (y tan(z)-e)dx + dy = 0 a) ecos(x) b) - cos(x) c) esin(z) d) 4 c) dz 1 da 1 x -N11 Т d) 2 dz dr T 2 d) z² - 2xy-y²=C d) - sin(x)
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