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 $3 .$