Q. 94.5( 2 Votes )

Mark the correct alternative in each of the following:

The order of the differential equation whose general solution is given by

y = c1cos (2x + c2) – (c3 + c4) ax+ c5 + c6 sin (x – c7) is

A. 3

B. 4

C. 5

D. 2

Answer :

y = c1cos (2x + c2) – (c3 + c4) ax+ c5 + c6 sin (x – c7)

y = c1 [cos(2x). cos c2 – sin (2x). sin c �2] – (c3 + c4) ac5. ax + c6[sin (x). cos c7 – cos (x). sin c7)

y = c1.cos c2 . cos(2x)– c1. sin c �2. sin (2x)– (c3 + c4) ac5. ax +c6. cos c7 � �. sin (x) – c6. sin c7.cos (x)

Now, c1.cos c2,c1. sin c �2, (c3 + c4) ac5, c6. cos c7 � �, c6. sin c7 are all constants

c1.cos c2 = A

c1. sin c �2 = B

(c3 + c4) ac5 = C

c6. cos c7 = D

c6. sin c7 = E

y = A. cos(2x)– B. sin (2x)– C. ax +D � �. sin (x) – E. cos (x)

Where A, B, C, D and E are constants

Since there are 5 constants, we have to differentiate y w.r.t x five times.

So, the Order of the differential equation = 5

= (C)

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