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 = c_{1}cos (2x + c_{2}) – (c_{3} + c_{4}) a^{x}^{+ c5} + c_{6} sin (x – c_{7}) is

A. 3

B. 4

C. 5

D. 2

Answer :

y = c_{1}cos (2x + c_{2}) – (c_{3} + c_{4}) a^{x}^{+ c5} + c_{6} sin (x – c_{7})

⇒ y = c_{1} [cos(2x). cos c_{2} – sin (2x). sin c �_{2}] – (c_{3} + c_{4}) a^{c5}. a^{x} + c_{6}[sin (x). cos c_{7} – cos (x). sin c_{7})

⇒ y = c_{1}.cos c_{2 .} cos(2x)– c_{1}. sin c �_{2}. sin (2x)– (c_{3} + c_{4}) a^{c5}. a^{x} +c_{6}. cos c_{7 � �}. sin (x) – c_{6}. sin c_{7.}cos (x)

Now, c_{1}.cos c_{2},c_{1}. sin c �_{2}, (c_{3} + c_{4}) a^{c5}, c_{6}. cos c_{7 � �}, c_{6}. sin c_{7} are all constants

∴ c_{1}.cos c_{2} = A

c_{1}. sin c �_{2} = B

(c_{3} + c_{4}) a^{c5} = C

c_{6}. cos c_{7} = D

c_{6}. sin c_{7} = E

⇒ y = A. cos(2x)– B. sin (2x)– C. a^{x} +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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