# IIT JAM Mathematics Test Series 2023 : Differential Equations – Bernoulli’s Differential Equation

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## IIT JAM Mathematics Test Series 2023 : Differential Equations – Bernoulli’s Differential Equation

Q1. Which of the following is the correct representation of the Bernoulli’s Differential Equation ?

• (a) dx/dy + P1 x = Q1 xn
• (b) dx/dy + P1 x = Q1 x
• (c) dx/dy – P1 x = Q1 xn
• (d) dx/dy – P1 x = Q1 x

Q2. Solve the Bernoulli’s Differential equation :

(dy/dx) + x sin 2y = x3 cos2 y

• (a) cot y = (1/2) × (x2– 1) + ce-x2
• (b) tan y = (1/2) × (x2– 1) + ce-x2
• (c) tan y = (1/2) × (x2+ 1) + cex2
• (d) cot y = (1/2) × (x2+ 1) + cex2

Q3. Solve the Bernoulli’s Differential equation :

(dy/dx) = ex–y (ex– ey)

• (a) ex (ey– ex + 1) = c
• (b) eex (ex– ey + 1) = c
• (c) eex (ey– ex + 1) = c
• (d) ey (ey– ex + 1) = c

Q4. Solve the Bernoulli’s Differential equation :

dz/dx + log zz/x = z/x2 (log z)²

• (a) 1/(log z) = 1/2x2 + c
• (b) 1/x(log z) = 1/x2 + c
• (c) 1/x(log z) = 1/x2 – c
• (d) 1/x(log z) = 1/2x2 + c

Q5. Solve the Bernoulli’s Differential equation :

x (dy/dx) + y log y = xy ex

• (a) y2x2 = 2x3/3x4/4 + c
• (b) y2/x2 = 2x3/3x4/4 + c
• (c) y2x2 = 2x4/3x3/4 + c
• (d) y2x2 = 2x4/3 + x3/4 – c

Q6. Solve the Bernoulli’s Differential equation :

dy/dx = (x2 + y2 + 1)/2xy

given y = 1 when x = 1

• (a) y2 = x (x – 1) + 1
• (b) y2 = x (x + 1) – 1
• (c) x2 = y (x + 1) – 1
• (d) x2 = x (x – 1) + 1

Q7. Solve the Bernoulli’s Differential equation :

dy/dx + (1/x) sin 2y = x2 cos2 y

• (a) x tan y = c – ( x5/5)
• (b) tan y = c + ( x5/5)
• (c) x2 tan y = c + ( x5/5)
• (d) x tan y = c – ( x5/5)

Q8. Solve the Bernoulli’s Differential equation :

(sec x tan x tan y – ex) dx + sec x sec2 y dy = 0

• (a) cot y sec x = ex – c
• (b) sec y cot x = ey + c
• (c) tan x sec y = ex – c
• (d) tan y sec x = ex + c

Q9. Solve the Bernoulli’s Differential equation :

sin y (dy/dx) = cos y (1 – x cos y)

• (a) sec y = x + 1 + cex
• (b) tan y = x + 1 + cex
• (c) sec y = x – 1 – cex
• (d) tan y = x – 1 – cex

Q10. Solve the Bernoulli’s Differential equation :

(dy/dx) + (1/x) tan y = (1/x2) tan y sin y

• (a) x sec y = c + log x
• (b) x cosec y = c + log x
• (c) x cos y = c + log x
• (d) cosec y = c – log x

Q11. Solve the Bernoulli’s Differential equation :

(dy/dx) + 1 = ex–y

• (a) ex = ce–y + (1/2) × ey
• (b) ey = ce–x – (1/2) × ex
• (c) ey = ce–x + (1/2) × ex
• (d) ex = ce–x – (1/2) × ey

Q12. Solve the Bernoulli’s Differential equation :

(dy/dx) – (tan y)/(1 + x) = (1 + x) ex sec y

• (a) sin x = (1 – y) (c + ey)
• (b) cos y = (1 + x) (c + ex)
• (c) cos y = (1 – y) (c + ey)
• (d) sin y = (1 + x) (c + ex)

Q13. Solve the Bernoulli’s Differential equation :

(dy/dx) + (1/x) = ey/x2

• (a) 2x e–y = 1 + 2cx2
• (b) 2x e–x = 1 + 2cx2
• (c) 2y e–y = 1 + 2cy2
• (d) 2y e–x = 1 + 2cy2

Q14. Solve the Bernoulli’s Differential equation :

(x2 + y2 + 2x) dx + 2y dy = 0

• (a) ey (y2 – x2) = c
• (b) ex (x2 + y2) = c
• (c) ey (x2 – y2) = c
• (d) ex (x2 – y2) = c

Q15. Solve the Bernoulli’s Differential equation :

(xy2 + e-1/x3) dx – x2y dy = 0

• (a) y2/x2 = (3/2) × e1/x3 + c
• (b) y2/x2 = (2/3) + e1/x3 + c
• (c) y2/x2 = (2/3) × e-1/x3 + c
• (d) y2/x2 = (3/2) × e-1/x3 – c

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