11. The differential equation 2.r-yd:r + (x 2 + 1)dy = 0 is Select the correct a
ID: 2985222 • Letter: 1
Question
11. The differential equation 2.r-yd:r + (x 2 + 1)dy = 0 is
Select the correct answer.
(a) exact with solution x.:2y + y + c
(b) exact with solution :1: y + y = c
(c) exact with solution 2xy + y + c
(d) exact with solution 2:ry + y = c
(e) not exact
12. The differential equation :J;ydx + (.r-2 + y 2 )dy = 0 is Select the correct answer.
(a) exact with solution :1: yj2 + :ti/ 3 = c
(b) exact with solution :1:2 y /2 + y 2 / 2 = c
(c) exact with solution x 2 yj2 + y 3 / 3 + c
(d) not exact but having an integrating factor :r
(e) not exact but having an integrating factor y
13. The differential equation (x + 2y)dx + ydy = 0 can be solved using the substitution Select the correct answer .
(a) n = :1; + 2y
(b) ll = y
(c) u, = :ry
(d) a= yjx
(e) it cannot be solved using a substitut ion
14. The solution of (:r + 2y)dx + ydy = 0 is Select the correct answer.
(a) ln :c + ln(y + x) = c
(b) ln ((y + 1:)j:1:) = c
(c) ln(y+ ::c)+ .r-j(y+x)=c
(d) ln(y + :r:) + :r:j(y + :r) + c
(e) it cannot be solved
15. The differential equation y' - y j:1: = y 2 can be solved using the substitution Select the correct answer.
(a) n=y
(b) u=:t/
(c) u = 7/
(d) a= y - 1
(e) u = y -2
16. The solution of the differential equation y'- yj.T = y 2 is Select the correct answer.
(a) !J = cj x - x/2
(b) y = 1/ (cj x - x/2) (c) y = (c.1: - :r: ln :r)
(d) !J = 1/ (c.T - x ln x)
(e) y = 1 +CCX
17. The differential equation y' = (4x + 2y + 3)2 has the solution
Select the correct answ r.
(a) y = -(4x + :1)3/12 + c
(b) ]j = (4.T + 2y + )) : /12 + C
(c) y=(4x+2y+3) 3/3+c
(d) y = v'2tan(2v'2x +c)
(e) 4x + 2y + 3 = /2 tan(2/2:r +c)
18. The differential equ ation y' = vlx + y + 1 - 1 has the solution
Select the correct answer.
(a) y = ((x + c)/2)2
(b) ]j = 2(.T -1- ]j -1- 1)3/ 2 /3 + r:
(c) x+y+l=(( :r+c)/2) 2
(d) y=2(x+y+l) 312 j3-:r+c (e) :c + y = ((x + c)/2) 2
19. Solve the problemy'= (x + l)y, y(O) = 1 numerically for y(0.2) using h = 0.1.
Select the correct answer .
(a) 1.1
(b) 1.11
(c) 1.2
(d) 1.21
(e) 1.221
20. Solve the problem y' = 1 2 y
Select the correct answer.
(a) 1.0
(b) 1.001
(c) 1.01
(d) 1.02
(e) 1.002
Explanation / Answer
11-d
12-c
13-e
14-d
15-e
16-b
17-e
18-c
19-d
20-d
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