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The number of arbitrary constants in the particular solution of a differential equation of third order are:
In a particular solution of a differential equation, there is no arbitrary constant.
In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
y = ex + 1 : y′′ – y′ = 0
y = x2 + 2x + C : y′ – 2x – 2 = 0
y = cos x + C : y′ + sin x = 0
y = Ax : xy′ = y (x ≠ 0)
y = x sin x : xy′ = y + x (x ≠ 0 and x > y or x < – y)
xy = log y + C :
y – cos y = x : (y sin y + cos y + x)y′ = y
x + y = tan–1y : y2y′ + y2 + 1 = 0
The number of arbitrary constants in the general solution of a differential equation of fourth order are: