MCQ on Method of Separation of Variables with Answers

Practice MCQ on Method of Separation of Variables with Answers

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MCQ on Method of Separation of Variables with Answers


Q1. Solve the Differential Equation : dy/dx = (x – y + 3)/(2x – 2y + 5)

(a) x – y + 2 = ce2y–x
(b) x – y – 2 = ce2y–x
(c) x + y + 2 = ce2y–x
(d) x + y + 2 = ce2y–x


Q2. Solve the Differential Equation : (2x + 4y + 3) (dy/dx) = 2y + x + 1.

(a) 4x + 8y + 5 = ce8(x – 2y)
(b) 4x + 8y + 5 = ce4(x – 2y)
(c) 4x + 8y + 5 = ce4(x – y)
(d) 4x – 8y + 5 = ce4(x – 2y)


Q3. Solve the Differential Equation : (4x + 6y + 5z)dx/(4x + 6y + 5z)dy = 1

(a) (2/7) (2x + 3y) + (9/49) log (14x + 21y + 22) = x – c
(b) (2/7) (2x + 3y) – (9/49) log (14x – 21y + 22) = x + c
(c) (2/7) (2x + 3y) – (9/49) log (14x + 21y + 22) = x + c
(d) (2/7) (2x – 3y) – (9/49) log (14x + 21y + 22) = x + c


Q4. Solve the Differential Equation : (x – y)2 (dy/dx) = a2

(a) y – c = (a/2) log {(x – y – a)/(x – y + a)}
(b) y + c = (a/2) log {(x – y + a)/(x – y + a)}
(c) y + c = (a/2) log {(x – y – a)/(x – y – a)}
(d) y + c = (a/2) log {(x – y – a)/(x – y + a)}


Q5. Solve the Differential Equation : (x + y – a)dx/(x + y – b)dy = (x + y + a)/(x + y + b)

(a) (b – a)2 log {(x + y)2 – ab} = 2 (x – y) + c
(b) (b – a)2 log {(x + y) – ab} = 2 (x – y) + c
(c) (b – a)2 log {(x + y)2 – ab} = 2 (x + y) + c
(d) (b – a)2 log {(x + y)2 + ab} = 2 (x – y) + c


Q6. Solve the Differential Equation : dy/dx + 1 = ex+y

(a) x – e–(x + y) = c
(b) x + e–(x + y) = c
(c) x + e(x + y) = c
(d) x + e(x – y) = c


Q7. Solve the Differential Equation : sin–1 (dy/dx) = x + y

(a) –2/(x – c) = 1 + tan 1/2 (x + y)
(b) 2/(x + c) = 1 + tan 1/2 (x + y)
(c) –2/(x + c) = 1 + tan 1/2 (x + y)
(d) 2/(x – c) = 1 + tan 1/2 (x – y)


Q8. Solve the Differential Equation : (x + y – 1)dy = (x + y)dx.

(a) 2(y + x) + log (2x + 2y + 1) = c
(b) 2(y – x) – log (2x – 2y – 1) = c
(c) 2(y + x) + log (2x + 2y – 1) = c
(d) 2(y – x) – log (2x + 2y – 1) = c


Q9. Solve the Differential Equation : dy/dx = (x + y + 1)/(x + y – 1) when y = (1/3) at x = (2/3).

(a) log (x + y) = y – x – (1/3)
(b) log (x – y) = y – x – (1/3)
(c) log (x – y) = y + x – (1/3)
(d) log (x + y) = y + x + (1/3)


Q10. Solve the Differential Equation : dy/dx = cos (x + y).

(a) x – c = tan {(x + y)/2}
(b) x + c = tan {(x + y)/2}
(c) x – c = tan {(x – y)/2}
(d) x + c = tan {(x + y)}


Q11. Solve the Differential Equation : (x + y + 1) (dy/dx) = 1.

(a) x + y – 2 = cey
(b) x – y – 2 = cex
(c) x + y + 2 = cey
(d) x + y + 2 = cex


Q12. Solve the Differential Equation : (x + 2y – 1) dx = (x + 2y + 1) dy

(a) 3x + 6y + 1 = ce3(x+y)/2
(b) 3x + 6y – 1 = ce3(x-y)
(c) 3x – 6y – 1 = ce3(x-y)/2
(d) 3x + 6y – 1 = ce3(x-y)/2


Q13. Solve the Differential Equation : dy/dx = (4x + 6y + 5) /(3y + 2x + 4)

(a) 3y – 6x + (9/8) log (16x + 24y + 23) = 8c
(b) 3y – 6x – (9/8) log (16x + 24y + 23) = 8c
(c) 3y – 6x + (9/8) log (16x – 24y – 23) = 8c
(d) 3y + 6x + (9/8) log (16x + 24y + 23) = 8c


Q14. Solve the Differential Equation : (x + y) (dx – dy) = dx + dy

(a) x + y + c = log (x + y)
(b) x – y + c = log (x + y)
(c) x – y – c = log (x – y)
(d) x + y – c = log (x – y)


Q15. Solve the Differential Equation : dx/dy = sec (x + y)

(a) y – tan 1/2 (x – y) = c
(b) y + tan 1/2 (x + y) = c
(c) y – tan 1/2 (x + y) = c
(d) y + tan 1/2 (x – y) = c


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Answer Key

01.(a)06.(b)11.(c)
02.(b)07.(c)12.(d)
03.(c)08.(d)13.(a)
04.(d)09.(a)14.(b)
05.(a)10.(b)15.(c)

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