Differential Equations Question 210
Question: The order of the differential equation whose general solution is given by $ y=C_1{e^{2x+C_2}}+ $
$ C_3e^{x}+C_4\sin (x+C_5) $ is
[AMU 2000]
Options:
A) 5
B) 4
C) 3
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=C_1{e^{2x+C_2}}+C_3e^{x}+C_4\sin (x+C_5) $
$ =C_1.{e^{C_2}}e^{2x}+C_3e^{x}+C_4(\sin x\cos C_5+\cos x\sin C_5) $
$ =Ae^{2x}+C_3e^{x}+B\sin x+D\cos x $
Here, $ A=C_1{e^{C_2}} $ , $ B=C_4\cos C_5 $ , $ D=C_4\sin C_5 $
(Since equation consists of four arbitrary constants) \ order of differential equation = 4.
BETA
