Differential Equations: Class 12 Previous Year Questions

Differential Equations questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. The order and degree of the differential equation d dx(ey) = 0 respectively are 1 (A) 0, 1 (B) 1, 1 (C) 2, 1 (D) 1, not defined      
   Board 20261 markMCQRepeated: 2022,2023,2026
2. { } 29. (a) Find the general solution of the following differential equation : 3 x2 dy dx = x2 + xy + y2 OR (b) Find the particular solution of the differential equation 3 xy dy dx = (x + 2) (y + 2), given that y(1) = –1. 16 { } 30.     (L…
   Board 20263 marksshort answerRepeated: 2022,2026
3. { } 29. (a) Solve the following differential equation : 3 x x d dy = y – x sin2       x y , given that y(1) = 6  OR (b) Find the general solution of the differential equation : y log y dy dx + x = y 2 . 3 16 { } 30.       …
   Board 20263 marksshort answerRepeated: 2022,2026
4. If p and q are respectively the order and degree of the differential equation (dy = O, then (p - q) is dx((dx· (A) (B) (C) (D) ASSERTION - REASON BASED QUESTIONS Direction : Question number 19 and 20 are Assertion (A) and Reason (R) based questions. Two statem…
   Board 20251 markAssertion-ReasonRepeated: 2025,2026
5. dy 6. Degree of the differential equation sin x + cos dx (A) (B) (C) not defined (D) Page 5 3 (1 -y2 dx 7. +yx= ay, (- 1<y<1) m : dy (A) y²-1 (B) y2- 1 (C) 1-y2 (D) V1-y2 8. Q: (2, 1, -1) (4, 4, -7) , (A) 2i + 3j - 6k (B) -2i - 3 + 6k -2i _ 3i + 6k 2 + i_ 6 (C…
   Board 20231 markMCQRepeated: 2023,2026
6. Find the particular solution when x = y = 0 for the following differential equation. Show your steps. OR Find the general solution of the following differential equation. Show your steps.
   CBSE practice 2022-233 marksshort answerRepeated: 2022,2026
7. { } 11. The integrating factor of differential equation R dy dx + Px = Q where P, Q, R are functions of y is 1 (A) dy Q P e (B) Pdy e (C) dy R P e (D) x d R P e 8 { } 12.   d dx(ey) = 0    , :  1 (A) 0, 1 (B) 1, 1 (C) 2, 1 (D) 1…
   Board 20261 markMCQ
8. { } 11. The general solution of the differential equation x x y d dy  is 1 (A) log y = log x + C (B) y + x = C (C) y – x = C (D) log y + log x = C 8 { } 12.   2x x d dy – y = 3     1 (A) x (B) x 1 (C) ex (D) e–x 13.  | a | = 5  …
   Board 20261 markMCQ
9. (a) Solve the differential equation 2(y + 3) - xy dx OR (b) Solve the following differential equation : + 2xy = 4x2. (1 + x2)- dx
   Board 20253 marksshort answer
10. The integrating factor of differential equation (x + 2y3) 12. = 2y is dx (A) e2 (B) /y (C) (D) Page 7 of 24 A= 13. 10 (A) 0 (B) 1 (C)7 (D) ± 7 14. (272)·(15,20) (40, 15)=189, (A) (2, 72) 3, (15, 20) 1 (B) (15, 20) , (40, 15) 1 (C) (40, 15) , (15, 20) 1 (D) (40…
    Board 20251 markMCQ
11. Which of the following is not a homogeneous function of x and y ? y2 - xy (B) (A) x-3y (C) sin2 + (D) tan x - sec y
    Board 20251 markMCQ
12. (a) Find the general solution of the differential equation : (·xy - x2) dy = y2 dx. OR (b) Find the general solution of the differential equation :
    Board 20233 marksshort answer
13. The sum of the order and the degree of the differential equation y sin dx dy dx y d 3 2 2 is : (a) 5 (b) 2 (c) 3 (d) 4 ^ ^ ^ ^ ^ ^
    Board 20231 markMCQ
14. JJJJ Page 12 28. (H$) AdH$b g_rH$aU dx dy + sec2 x . y = tan x . sec2 x H$m {d{eîQ> hb kmV H$s{OE, {X`m J`m h¡ {H$ y(0) = 0. AWdm (I) AdH$b g_rH$aU x dy y dx 2 2 y x dx = 0 H$mo hb H$s{OE & (b) Check whether the lines given by equations x = 2 + 2, y = 7 + 1, z…
    Board 20233 marksshort answer
15. Find the sum of the order and the degree of the differential equation : dy (dy +1 dx) (dx)
    Board 20221 markvery short
16. Which of the following differential equation has an order of 2 and a degree of 3? 1 A. B. C. D.
    CBSE practice 2022-231 markMCQ
17. In which of the following differential equations is the degree equal to its order? (a) (b) (c) (d)
    CBSE practice 2023-241 markMCQ
18. The integrating factor of the differential equation   log 2 log dy x x y x dx   is (a) xe (b) log x (c) log (log x) (d) x
    CBSE practice 2023-241 markMCQ
19. Shown below is a differential equation. Find the order and the degree of the given differential equation. Give reasons to support your answer.
    CBSE practice 2021-222 marksshort answer
20. Kapila is trying to find the general solution of the following differential equations. Which of the above become variable separable by substituting y = b.x, where b is a variable? (a) only (i) (b) only (i) and (ii) (c) all - (i), (ii) and (iii) (d) None of the…
    CBSE practice 2023-241 markMCQ

Practise all 35 Differential Equations questions with answers →

Other Class 12 Maths chapters

Frequently asked questions