Q. 27

How many arbitrary constants are there in the general solution of the differential equation of order 3.

Answer :

Let any differential equation of order 3 be



Here A is any constant.


Now, to know the number of arbitrary constants in the general solution we integrate both sides of equation (1)




Again integrating




Again integrating




is the general solution of the differential equation with 3 arbitrary constants C1, C2, C3.


There are 3 arbitrary constants in the general solution of the differential equation of order 3.


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