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
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)