Question

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

Answer 1

Hint: - Arbitrary constants in the particular solution of a differential equation of third order is zero.

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 $=0$.
Now we have to find out the number of arbitrary constants in a particular solution of a differential equation.
$\therefore$Option (a) is correct.

Note: -Whenever we face such types of questions the key concept we have to remember is that the number of arbitrary constants in general solution is the order of the differential equation and the number of arbitrary constants in the particular solution is always zero.