CLASS : XII | BATCH: 2 YR JEE 2023
TOPIC: Differential Equations DPP NO. - 5
dy
1. The solution of the differential equation x = y (log y – log x + 1) is-
dx
[A] y = xecx [B] y + xecx = 0 [C] y + ex = 0 [D] None of these
dy xy
2. The solution of the equation = x y is-
dx
1 1
tan (y / x)
[A] c (x2 + y2)1/2 + e 0 [B] c (x2 + y2)1/2 = e tan (y / x)
1
tan (y / x)
[C] c (x2 – y2) = e [D] None of these
3. The solution of the differential equation (x2 + y2) dx = 2 xy dy is-
[A] x = c (x2 + y2) [B] x = c (x2 – y2) [C] x + c (x2 + y2)=0 [D] None of these
dy y
4. The solution of the equation x = y – x tan is -
dx x
x y
[A] x sin y + c = 0 [B] x sin y + c = 0 [C] x sin = c [D] None of these
x
dy x
5. The solution of the equation = 2y x is-
dx
[A] (x – y) (x + 2y)2 = c [B] y = x + c
x
[C] y = (2y – x) + c [D] y = + c
2y x
dy y
6. The solution of the differential equation, + = x2 is-
dx x
1
[A] 4xy = x4 + c [B] xy = x4 + c [C] xy = x4 + c [D] xy = 4x4 + c
4
dy
7. The solution of the differential equation + y = cos x is-
dx
1 1
[A] y = (cos x + sin x) + ce– x [B] y = (cos x – sin x) + ce– x
2 2
[C] y = cos x + sin x + ce–x [D] None of these
1
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dy
8. The solution of the differential equation x log x + y = 2 log x is-
dx
[A] y = log x + c [B] y = log x2 + c [C] y log x = (log x)2 + c [D] y = x log x + c
dy
9. The solution of the equation x + 3y = x is-
dx
x4 x4 x4
[A] x3 y + + c = 0 [B] x3y = + c [C] x3 y + = 0 [D] None of these
4 4 4
dy
10. The solution of the differential equation + y cot x = 2 cos x is-
dx
[A] y sin x + cos 2x = 2c [B] 2 y sin x + cos x = c
[C] y sin x + cos x = c [D] 2y sin x + cos 2x = c
11. The solution of (1 + y2) dx = (tan–1 y – x) dy is -
1 1 1
[A] x e tan y
= e tan y
(tan–1 y – 1) + c [B] x e tan y
= (tan–1 y + 1) – c
1
[C] x e tan y
= (tan–1 y – 1) + c [D] None of these
dy
12. The integrating factor of the differential equation (x log x) + y = 2 log x is-
dx
[A] log x [B] log (log x) [C] ex [D] x
13. The equation of the curve passing through the origin and satisfying the differential equation
dy
(1 + x2) + 2xy = 4x2 is-
dx
[A] (1 + x2) y = x3 [B] 2(1 + x2) y = 3x3 [C] 3(1 + x2)y = 4x3 [D] None of these
dy
14. The solution of the differential equation x + y = x2 + 3x + 2 is-
dx
x3 3 2 x4
[A] xy = + x + 2x + c [B] xy = + x3 + x 2 + c
3 2 4
x4 x3 x4
[C] xy = + + x2 + c [D] xy = + x3 + x 2 + cx
4 3 4
dy 1
15. The solution of the equation = is-
dx x y 1
[A] x = cey – y – 2 [B] y = x + cey – 2 [C] x + cey – y –2 = 0 [D] None of these
dy
16. Integrating factor of the differential equation + y tan x – sec x = 0 is-
dx
1 1
[A] esin x [B] [C] [D] ecos x
sin x cos x
2
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dy
17. The solution of differential equation + 1 = ex–y is-
dx
[A] ey = ex/ 2 + ce–x [B] ey = ex + ce–x [C] 3ey = ex/ 2 + ce–x [D] None of these
dy 1 cos 2y
18. The general solution of the differential equation + = 0, is given by -
dx 1 – cos 2x
[A] tan y + cot x = c [B] tan y – cot x = c [C] tan x – cot y = c [D] tan x + cot y = c
dy 1– y2
19. The solution of + 1– x2 = 0, is -
dx
[A] tan–1 x + cot–1 x = c [B] sin–1 x + sin–1 y = c [C] sec–1x + cosec–1x = c[D] None of these
dy
20. The solution of + y tan x = sec x is -
dx
[A] y sec x = tan x + c [B] y tan x = sec x + c [C] tan x = y tan x + c [D] x sec x = y tan y + c
ANSWERS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A B B C A A A C B D A A C A A C A B B A
3
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