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verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides of this equation with respect to x, we get:
Substituting the value of
in the given differential equation, we get:
L.H.S. =
= R.H.S.
Hence, the given function is the solution of the corresponding differential equation.
The numbers of arbitrary constants in the particular solution of a differential equation of third order are:
(A) 3 (B) 2 (C) 1 (D) 0
In a particular solution of a differential equation, there are no arbitrary constants.
Hence, the correct answer is D.
verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides of this equation with respect to x, we get:
Now, differentiating equation (1) with respect to x, we get:
Substituting the values of
in the given differential equation, we get the L.H.S. as:
Thus, the given function is the solution of the corresponding differential equation.
verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides of this equation with respect to x, we get:
Substituting the value of
in the given differential equation, we get:
L.H.S. =
= R.H.S.
Hence, the given function is the solution of the corresponding differential equation.
verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides of the equation with respect to x, we get:
L.H.S. = R.H.S.
Hence, the given function is the solution of the corresponding differential equation.
verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides with respect to x, we get:
Substituting the value of
in the given differential equation, we get:
Hence, the given function is the solution of the corresponding differential equation.
verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides of this equation with respect to x, we get:
Substituting the value of
in the given differential equation, we get:
Hence, the given function is the solution of the corresponding differential equation.
verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides of this equation with respect to x, we get:
L.H.S. = R.H.S.
Hence, the given function is the solution of the corresponding differential equation.
verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides of the equation with respect to x, we get:
Substituting the value of
in equation (1), we get:
Hence, the given function is the solution of the corresponding differential equation.
verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides of this equation with respect to x, we get:
Substituting the value of
in the given differential equation, we get:
Hence, the given function is the solution of the corresponding differential equation.
verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
Differentiating both sides of this equation with respect to x, we get:
Substituting the value of
in the given differential equation, we get:
Hence, the given function is the solution of the corresponding differential equation.
The numbers of arbitrary constants in the general solution of a differential equation of fourth order are:
(A) 0 (B) 2 (C) 3 (D) 4
We know that the number of constants in the general solution of a differential equation of order n is equal to its order.
Therefore, the number of constants in the general equation of fourth order differential equation is four.
Hence, the correct answer is D.
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