alleryThe number of arbitrary constants in the general solution of a differential equation of order $n$ is:
A$n$
B$0$
C$1$
D$n - 1$
Answer & Solution
Correct answer: A. $n$
By definition, the general solution of an $n$-th order differential equation contains exactly $n$ independent arbitrary constants, matching the order of the equation.
For example, $\dfrac{d^2y}{dx^2} + y = 0$ has the general solution $y = A\cos x + B\sin x$ with two constants $A$ and $B$, since the equation is of order 2.
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