Question

The order of the differential equation whose general solution is given by $y=\left(c_1+c_2\right)\cos \left(x+c_3\right)-c_4{e}^{x_{-}{c}_5}$, where $c_1,c_2,c_3,c_4,c_5$ are arbitrary constants, is

• A. 4
• B. 3
• C. 2
• D. 5

Answer 1

Answer: (B)

Given,
$y=\left(c_1+c_2\right)\cos \left(x+c_3\right)-c_4{e}^{x+c_5}$
$\Rightarrow y=\left(c_1\cos c_3+c_2\cos c_3\right)\cos x$
$=\left(c_1\sin c_3+c_2\sin c_3\right)\sin x-c_4{e}^{c_5}{e}^x$
$\Rightarrow y=A\cos x-B\sin x\cdot C{e}^x$
where, $A=c_1\cos c_3+c_2\cos c_3$
$B=c_1\sin c_3+c_2\sin c_3$ and
$C=-c_4{e}^{c_5}$
Which is an equation containing three arbitrary constant. Hence, the order of the differential equation is $3.$