# Linear differential equations with constant coefficients mcq

## Linear differential equations with constant coefficients mcq

Linear differential equations with constant coefficients mcq questions and answers for multiple choice questions test. Linear differential equations (LDE) with constant coefficients is a topic of Engineering Mathematics 3 (M3) for online exams of various universities. We are trying to provide you m3 linear differential equation mcq pdf for download the mcqs.

1.If the roots m1, m2, m3, â€¦, mn of auxiliary equation Ï†(D) = 0 are real and distinct, then solution of Ï†(D) y = 0 is â€¦â€¦â€¦â€¦
(A) c1em1x + c2em2x + â€¦ + cnemnx
(B) c1 cos m1x + c2 cos m2x + â€¦ + cn cos mnx
(C) m1ec1x + m2ec2x + â€¦ + mncnx
(D) c1 sin m1x + c2 sin m2x + â€¦ + cn sin mnx

c1em1x + c2em2x + â€¦ + cnemnx

2.The roots m1, m2, m3 â€¦, mn of auxiliary equation Ï†(D) = 0 are real. If two of these roots are repeated say m1 = m2 and theremaining roots m3, m4, â€¦, mn are distinct then solution of Ï†(D) y = 0 is â€¦â€¦â€¦â€¦
(A) c1em1x + c2m2x + â€¦ + cnmnx
(B)(c1x + c2) cos m1x + c3 cos m3x + x â€¦ + cn cos mnx
(C)(c1x + c2) em1x + c3em3x + â€¦ + cnemnx
(D)(c1x + c2) sin m1x + c3 sin m3x + â€¦ + cn sin mnx

(c1x + c2) em1x + c3em3x + â€¦ + cnemnx

3.The roots m1, m2, m3 â€¦, mn of auxiliary equation Ï†(D) = 0 are real. If three of these roots are repeated, say, m1 = m2 = m3 andthe remaining roots m4, m5, â€¦ mn are distinct then solution of Ï†(D) y = 0 is â€¦â€¦â€¦â€¦
(A) c1em1x + c2m2x + â€¦ + cn emnx
(B)(c1x2 + c2x + c3) em1x + c4em4x + â€¦ + cnemnx
(C)(c1x2 + c2x + c3) cos m1x + c4 cos m4x + â€¦ + cn cos mnx
(D)(c1x2 + c2x + c3) sin m1x + c4 sin m4x + â€¦ + cn sin mnx

(c1x2 + c2x + c3) em1x + c4em4x + â€¦ + cnemnx

4.If m1 = Î± + iÎ² and m2 = Î± – iÎ² are two complex roots of auxiliary equation of second order DE Ï†(D) y = 0 then it’s solution isâ€¦â€¦â€¦â€¦
(A) eÎ²x [c1 cos Î±x + c2 sin Î±x]
(B) eÎ±x [(c1x + c2) cos Î²x + (c3x + c4) sin Î²x]
(C) c1eÎ±x + c2eÎ²x
(D) eÎ±x [c1 cos Î²x + c2 sin Î²x]

eÎ±x [c1 cos Î²x + c2 sin Î²x]

5.If the complex roots m1 = Î± + iÎ² and m2 = Î± – iÎ² of auxiliary equation of fourth order DE Ï†(D) y = 0 are repeated twice thenit’s solution is â€¦â€¦â€¦â€¦
(A) eÎ²x [c1 cos Î±x + c2 sin Î±x]
(B) eÎ±x [(c1x + c2) cos Î²x + (c3x + c4) sin Î²x]
(C)(c1x + c2) eÎ±x + (c3x + c4) eÎ²x
(D) eÎ±x [c1 cos Î²x + c2 sin Î²x]d2ydy

eÎ±x [(c1x + c2) cos Î²x + (c3x + c4) sin Î²x]

6.The solution of differential equation d2y/dx2  – 5 dy/dx + 6y = 0 is â€¦â€¦â€¦â€¦
(A) c1e2x + c2e – 3x
(B) c1e-2x + c2e3x
(C) c1e-2x + c2e-3x
(D) c1e2x + c2e3xd2ydy

c1e2x + c2e3xd2ydy

7.The solution of differential equation d2y/dx2 – 5 dy/dx – 6y = 0 is â€¦â€¦â€¦â€¦
(A) c1e-x + c2e6x
(B) c1e-2x + c2e-3x
(C) c1e3x + c2e2x
(D) c1e-3x + c2e-2xd2y dy

c1e-x + c2e6x

8.The solution of differential equation 2 d2y/dx2  – dy/dx – 10y = 0 is â€¦â€¦â€¦â€¦55x
(A) c1e2x + c2e2 x
(B) c1e-2x + c2e- 2532 x
(C) c1e-2x + c2e2 x
(D) c1e-2x + c2ed2y

c1e-2x + c2e2 x

9.The solution of differential equation d2y/dx2  – 4y = 0 is â€¦â€¦â€¦â€¦
(A)(c1x + c2) e2x
(B) c1e4x + c2e-4x
(C) c1 cos 2x + c2 sin 2x
(D) c1e2x + c2e-2xd2y dy

c1e2x + c2e-2xd2y dy

10. The solution of differential equation d2y/dx2  – dy/dx – 2y = 0 is â€¦â€¦â€¦â€¦
(A) c1e2x + c2ex
(B) c1e2x + c2e-x
(C) c1e-2x + c2ex
(D) c1e-2x + c2e-x(A.1)

c1e2x + c2e-x

## Engineering Mathematics 3 mcq

11. The solution of differential equation 2 d2y/dx2  – 5 dy/dx + 3y = 0 is â€¦â€¦â€¦â€¦33×32 xx
(A) c1ex + c2e2 x
(B) c1e2x + c2e-3x
(C) c1e-x + c2e
(D)c1e2 + c2ed2ydy

c1ex + c2e2 x

12. The solution of differential equation d2y/dx2  + 2 dy/dx + y = 0 is â€¦â€¦â€¦â€¦
(A) c1e2x + c2ex
(B) c1ex + c2e-x
(C)(c1x + c2) e-x
(D)(c1x + c2) exd2ydy

(c1x + c2) e-x

13. The solution of differential equation 4 d2y/dx2  – 4 dy/dx + y = 0 is â€¦â€¦â€¦â€¦xx- 2
(A) c1e2 + c2e
(B)(c1 + c2x) e-2xx
(C) c1 cos 2x + c2 sin 2x
(D)(c1 + c2x) e2d2ydy

(c1 + c2x) e2d2ydy

14. The solution of differential equation d2y/dx2  – 4 dy/dx + 4y = 0 is â€¦â€¦â€¦â€¦
(A)(c1x + c2) e2x
(B)(c1x + c2) e-2x
(C) c1e4x + c2e-4x
(D)c1e2x + c2e-2xd2ydy

(c1x + c2) e2x

15. The solution of differential equation d2y/dx2  + 6 dy/dx + 9y = 0 is â€¦â€¦â€¦â€¦
(A) c1e-6x + c2e-9x
(B)(c1x + c2) e-3x
(C)(c1x + c2) e3x
(D)c1e3x + c2e2xd2y

(c1x + c2) e-3x

16. The solution of differential equation d2y/dx2  + y = 0 is â€¦â€¦â€¦â€¦
(A) c1ex + c2e-x
(B)(c1x + c2) e-x
(C) c1 cos x + c2 sin x
(D)ex (c1 cos x + c2 sin x)d2y

c1 cos x + c2 sin x

17. The solution of differential equation d2y/dx2  + 9y = 0 is â€¦â€¦â€¦â€¦
(A) c1 cos 2x + c2 sin 2x
(B)(c1x + c2) e-3x
(C) c1e3x + c2e-3x
(D)c1 cos 3x + c2 sin 3xd2ydy

c1 cos 3x + c2 sin 3xd2ydy

18. The solution of differential equation d2y/dx2  + 6 dy/dx + 10y = 0 is â€¦â€¦â€¦â€¦
(A) e-3x (c1 cos x + c2 sin x)
(B) ex (c1 cos 3x + c2 sin 3x)
(C) c1e5x + c2e2x
(D) ex (c1 cos x + c2 sin x)d2y dy

e-3x (c1 cos x + c2 sin x)

19. The solution of differential equation d2y/dx2  + dy/dx + y = 0 is â€¦â€¦â€¦â€¦3ï£®ï£«ï£¶ï£«3ï£¶ï£¹
(A) ex (c1 cos x + c2 sin x)
(B) ex/2c1 cosx + c2 sinxï£°ï£­2ï£¸ï£­2ï£¸ï£»1â€“2 xï£®ï£«3ï£¶ï£«3ï£¶ï£¹
(C) eï£¯c1 cosï£¬ï£·x + c2 sinï£¬ï£·xï£º
(D) c1ex + c2e-xï£°ï£­2ï£¸ï£­2ï£¸ï£»d2ydy

eï£¯c1 cosï£¬ï£·x + c2 sinï£¬ï£·xï£º

20. The solution of differential equation 4 d2y/dx2  + 4 dy/dx + 5y = 0 is â€¦â€¦â€¦â€¦
(A) e-x (c1 cos 2x + c2 sin 2x)
(B) e-x/2 [c1 cos x + c2 sin x]
(C) e-2x (c1 cos x + c2 sin x)
(D) c1e-4x + c2e-5xd3yd2ydy

e-x/2 [c1 cos x + c2 sin x]

22. The solution of differential equation d3y/dx3  – 7 dy/dx – 6y = 0 is â€¦â€¦â€¦â€¦
(A) c1ex + c2e2x + c3e3x
(B) c1e-x + c2e-2x + c336x
(C) c1e-x + c2e2x + c3ex
(D) c1e-x + c2e-2x + c3e3xd3yd2y dy

c1e-x + c2e-2x + c3e3xd3yd2y dy

23. The solution of differential equation d3y/dx3  + 2 d2y/dx2  + dy/dx = 0 is â€¦â€¦â€¦â€¦
(A) c1 + ex (c2x + c3)
(B) c1 + e-x (c2x + c3)
(C) e-x (c2x + c3)
(D) c1 + c2ex + c3e-xd3yd2ydy

c1 + e-x (c2x + c3)

24. The solution of differential equationâ€¦â€¦â€¦â€¦ d3y/dx3  – 5 d2y/dx2  + 8 dy/dx – 4y = 0 is
(A) c1ex + (c2x + c3) e2x
(B) c1ex + c2e2x+c3e3x
(C)(c2x + c3) e2x
(D) c1e-x + (c2x + c3) e-2xd3ydy

c1ex + (c2x + c3) e2x

25. The solution of differential equation d3y/dx3  – 4 dy/dx = 0 is â€¦â€¦â€¦â€¦
(A) c1e2x + c2e-2x
(B) c1 + c2 cos 2x + csin 2x
(C) c1ex + c2e-2x + c3e-3x
(D) c1 + c2e2x + c3e-2xd3y

c1 + c2e2x + c3e-2xd3y

26. The solution of differential equation d3y/dx3  + y = 0 is â€¦â€¦â€¦â€¦1ï£«33ï£¶ï£«11ï£¶
(A) c1ex + exï£¬c2 cosï£·
(B) c1e-x + e2 xc2 cosï£­2 x + c3 sin2 xï£¸ï£­2 x + c3 sin 2 xï£¸1ï£«33ï£¶
(C) c1e-x + e2 xï£¬c2 cosï£·
(D)(c1 + c2x + c3x2) e-xï£­2 x + c3 sin2 xï£¸d3ydy

c1e-x + e2 xï£¬c2 cosï£·

27. The solution of differential equation d3y/dx3  + 3 dy/dx = 0 is â€¦â€¦â€¦â€¦
(A) c1 + c2 cos x + c3 sin x
(B) c1 + c2 cos3x + c3 sin3x
(C) c1 + c2e3x + c3e3x
(D) c1 cos x + c2 sin xd3y d2ydy

c1 + c2 cos3x + c3 sin3x

28. The solution of differential equationâ€¦â€¦â€¦â€¦ d3y/dx3  + d2y/dx2  – 2 dy/dx + 12y = 0 is
(A) c1e-3x + ex (c2 cos3x + c3 sin3x)
(B) c1e-3x + (c2 cos 3x + c3 sin 3x)
(C) c1e3x + e-x (c2 cos3x + c3 sin3x)
(D) c1e-x + c2e-3x + c3e3xd

c1e-3x + ex (c2 cos3x + c3 sin3x)

29. The solution of differential equation (D3 – D2 + 3D + 5) y = 0 where D =dx is â€¦â€¦â€¦â€¦
(A) c1e-x + ex (c2 cos 2x + c3 sin 2x)
(B) c1e-x + (c2 cos 3x + c3 sin 3x)
(C) c1ex + e-x (c2 cos 2x + c3 sin 2x)
(D) c1e-x + c2e-2x + c3e-3xd3y d2ydy

c1e-x + ex (c2 cos 2x + c3 sin 2x)

30. The solution of differential equation d3y/dx3  – d2y/dx2  + 4 dy/dx – 4y = 0 is â€¦â€¦â€¦â€¦
(A)(c1 + c2x) e-2x + c3e-x
(B) c1ex + c2 cos 4x + c3 sin 4x
(C) c1ex + c2 cos 2x + c3 sin 2x
(D) c1ex + c2e2x + c3e-2xd4y

c1ex + c2 cos 2x + c3 sin 2x

## Mathematics 3 mcq Computer Engineering

31. The solution of differential equation d4y/dx4  – y = 0 is â€¦â€¦â€¦â€¦
(A)(c1x + c2) e-x + c3 cos x + c4 sin x
(B)(c1x + c2) cos x + (c3x + c4) sin x
(C)(c1 + c2x + c3x2 + c4x3) ex
(D) c1ex + c2e-x + c3 cos x + c4 sin xd

c1ex + c2e-x + c3 cos x + c4 sin xd

32. The solution of differential equation (D4 + 2D2 + 1) y = 0 where D = dx is â€¦â€¦â€¦â€¦
(A)(c1x + c2) ex + (c3x + c4) e-x
(B)(c1x + c2) cos x + (c3x + c4) sin x
(C) c1ex + c2e-x + c3 cos x + c4 sin x
(D)(c1x + c2) cos 2x + (c3x + c4) sin 2x

(c1x + c2) cos x + (c3x + c4) sin x

33. The solution of differential equation (D2 + 9)2 y = 0, where D =(2)dx is â€¦â€¦â€¦â€¦
(A)(c1x + c2) e3x + (c3x + c4) e-3x
(B)(c1x + c2) cos 3x + (c3x + c4) sin 3x
(C)(c1x + c2) cos 9x + (c3x + c4) sin 9x
(D)(c1x + c2) cos x + (c3x + c4) sin xd4yd2y

(c1x + c2) cos 3x + (c3x + c4) sin 3x

34. The solution of differential equation d4y/dx4  + 8 d2y/dx2  + 16y = 0 is â€¦â€¦â€¦â€¦
(A) c1e2x + c2e-x + c3ex + c4e-2x
(B)(c1x + c2) e2x + (c3x + c4) e-2x
(C)(c1x + c2) cos 4x + (c3x + c4) sin 4x
(D)(c1x + c2) cos 2x + (c3x + c4) sin 2xd6yd4yd2y

(c1x + c2) cos 2x + (c3x + c4) sin 2xd6yd4yd2y

35. The solution of differential equation d6y/dx6  + 6 d4y/dx4  + 9 d2y/dx2  = 0 is â€¦â€¦â€¦â€¦
(A) c1x + c2 + (c3x + c4) cos3x + (c3x + c6) sin3x
(B) c1x + c2 + (c3x + c4) cos 3x + (c5x + c6) sin 3x
(C)(c1x + c2) cos3x + (c3x + c4) sin3x
(D) c1x + c2 + (c3x + c4) e3x.

c1x + c2 + (c3x + c4) cos3x + (c3x + c6) sin3x

Linear differential equations with constant coefficients mcq, linear differential equation with constant coefficient mcqs pdf, m3 linear differential equation mcq, lde mcq, m3 mcq electrical engineering, m3 mcq computer engineering, m3 mcq sppu, m3 mcq pune university, m3 mcq pdf, engineering mathematics 3 mcq, engineering mathematics 3 mcq pdf download, engineering mathematics 3 mcq pdf download computer engineering, engineering mathematics 3 mcq pune university,

error: Content is protected !!
Scroll to Top