Question

# The number of arbitrary constants in the particular solution of a differential equation of third order is${\text{a}}{\text{. 0}} \\ {\text{b}}{\text{. 1}} \\ {\text{c}}{\text{. 2}} \\ {\text{d}}{\text{. 3}} \\$

Order of differential equation $= 3$(given)
Number of arbitrary constants in the general solution of a differential equation is equal to the order of differential equation, while the number of arbitrary constants in a particular solution of a differential equation is always equal to$0$.
$\therefore$Number of arbitrary constants in the general solution of a differential equation$=$order of differential equation$= 3$
And the number of arbitrary constants in the particular solution of a differential equation $= 0$.
$\therefore$Option (a) is correct.