Updated By SaraNextGen

On March 11, 2024, 11:35 AM

Question 1:

Answer:

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.

Question 2:

Answer:

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.

Question 3:

Answer:

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.

Question 4:

Answer:

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.

Question 5:

Answer:

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.

Question 6:

Answer:

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.

Question 7:

Answer:

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.

Question 8:

Answer:

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.

Question 9:

Answer:

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.

Question 10:

Answer:

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.

Question 11:

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

Answer:

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.

Question 12:

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

Answer:

In a particular solution of a differential equation, there are no arbitrary constants.

Hence, the correct Answer is D.