9 Differential Equations. 9.1 Modeling with Differential Equations.
Test on Differential Equations
3
ACE ENGINEERING ACADEMY MATHEMATICS 7(6721',))(5(17,$/(48$7,216 1. The order of the d ifferential equation 1 + dy 3 = 3 d 2 y is dx dx 2 a) 1 b) 3 c) 2 d) 4 5 2. The degree of the differential equation dy 2 = dy is dx dx a) 1 b) 2 c) 3 d) 0 3. The equation (x 2 + y 2 + x) dx + xy dy = 0 a) homogenous b) linear in y c) exact d) none of the above 4. An integrating factor of (x 2 + y 2 + 1) dx – 2xy dy = 0 is a) 1/x 2 b) x c) y d) – x 2 5. An integratin g factor of dx + x dy = e -y logy dy is a) e y b) e x c) x d) e -x 6. 2xy dx – (x 2 + y 2 + 1) dx = 0 is a) Bernonth equation b) a linear equation c) an exact equation d) non-homog eneous equation 7. The orthogonal properties of xy = c is a) x 2 + y 2 = c b) xy = c c) x 2 – y 2 = c d) x 2 = c 8. An integrating factor of (dy/dx) – (6y / x ) = x is a) x -6 b) x c) y -6 d) x 2 9. The equation (x 2 – 2xy + 3y 2 ) dx + (4y 3 + 6xy – x 2 ) dy = 0 is a) linear b) homogeneou s c) exact d) non exact 10. If ay dx + bx dy = 0 is exact (a, b constant) then a) a – b = 0 b) a + b = 0 c) x = y d) x + y = 0 11. A differential equation will have a) only one solution b) infinite number of solutions c) solutions as many as order d) none of the above 12. For the differential equation y = x dy + 5 ; y 2 = 20 x is dx dy/dx a) the general solution b) a particular solution c) a singular solution d) none of the above 13. An integrating factor of y dx – x dy = 0 is a) 1/xy b) x 2 c) 1/x d) none of the above 14. The differential equation with (1, x, e x ) as the linearly indifferent solution is a) (D 3 + D + 1) y = 0 b) (D 3 - D) y = 0 c) (D 2 + D) y = 0 d) (D 3 + D 2 ) y = 0 (Contd…..2)
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Transcript of Test on Differential Equations
8/3/2019 Test on Differential Equations
http://slidepdf.com/reader/full/test-on-differential-equations 1/2
ACE ENGINEERING ACADEMY
MATHEMATICS
7(6721',))(5(17,$/(48$7,216
1. The order of the differential equation 1 + dy 3 = 3 d2y is
dx dx2
a) 1 b) 3 c) 2 d) 45
2. The degree of the differential equation dy 2 = dy isdx dx
a) 1 b) 2 c) 3 d) 0
3. The equation (x2 + y2 + x) dx + xy dy = 0
a) homogenous b) linear in y c) exact d) none of the above
4. An integrating factor of (x2 + y2 + 1) dx – 2xy dy = 0 isa) 1/x2 b) x c) y d) – x2
5. An integrating factor of dx + x dy = e-y logy dy isa) ey b) ex c) x d) e-x
6. 2xy dx – (x2 + y2 + 1) dx = 0 is
a) Bernonth equation b) a linear equationc) an exact equation d) non-homogeneous equation
7. The orthogonal properties of xy = c isa) x2 + y2 = c b) xy = c c) x2 – y2 = c d) x2 = c
8. An integrating factor of (dy/dx) – (6y / x) = x is
a) x-6 b) x c) y-6 d) x2
9. The equation (x2 – 2xy + 3y2) dx + (4y3 + 6xy – x2) dy = 0 isa) linear b) homogeneous c) exact d) non exact
10. If ay dx + bx dy = 0 is exact (a, b constant) then
a) a – b = 0 b) a + b = 0 c) x = y d) x + y = 0
11. A differential equation will have
a) only one solution b) infinite number of solutionsc) solutions as many as order d) none of the above
12. For the differential equation y = x dy + 5 ; y2 = 20 x is
dx dy/dx
a) the general solution b) a particular solutionc) a singular solution d) none of the above
13. An integrating factor of y dx – x dy = 0 is
a) 1/xy b) x2 c) 1/x d) none of the above
14. The differential equation with (1, x, ex) as the linearly indifferent solution is
a) (D3 + D + 1) y = 0 b) (D3 - D) y = 0 c) (D2 + D) y = 0 d) (D3 + D2) y = 0
(Contd…..2)
8/3/2019 Test on Differential Equations
http://slidepdf.com/reader/full/test-on-differential-equations 2/2
Æ ACEÆ :: 2 :: Æ ACEÆ
15. If the functions 1, e3x from the fundamental system of y11 + ay1 + by = 0 then
a) a = 3, b = 0 b) a = 0, b = 3 c) a = -3, b = 1 d) a = 0, b = -3
16. The differential equation of the family y = c isa) dy/dx = c b) dy/dx = 0 c) (dy/dx) + c = 0 d) none
17. An integrating function of dy – 5 y = 5x2 is
dx xa) x5 b) x-5 c) x d) x2
18. The solution of y1 + 5y = 2 ex, y(0) = 1 is
a) y = (1/3) (ex + 2 e-5x) b) y = (1/3) (ex - 2 e-5x)
c) y = (ex + 2 e-5x) b) none of the above
19. If 1, 2 are roots of auxiliary equation of f (D) y = X then f (D) = ---------- .a) (D – 1) (D + 2) b) (D – 1) (D – 2) c) D (D – 1) d) D (D – 2)
20. The particular integral of 1 cos3x = ---------.
(D2 + 9)
a) sin 3x b) x sin3x c) cos 3x d) x cos3x6 6 6 6
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KEY SHEET FOR TEST ON DIFFERENTIAL EQUATIONS
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