Question

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

• A. $5$
• B. $4$
• C. $3$
• D. $2$

Answer 1

The correct option is C $3$

We know that the order of a differential equation is equal to the number of arbitrary constants. The given differential equation is $y=(c_1+c_2)\cos (x+c_3)-c_4{e}^{x+c_5}.$

Rewriting the equation in terms of essential arbitrary constants:

$y=\left(K_1\right)\cos (x+K_2)-K_3{e}^x.$

where $K_1=c_1+c_2;K_2=c_3;K_3=c_4{e}^{c_5}.$

Hence the essential arbitrary constants are $3$.

$\therefore$ The order of the differential equation is $3$.