Mathematics Part-II

Book: Mathematics Part-II

Chapter: 9. Differential Equations

Subject: Maths - Class 12th

Q. No. 11 of Exercise 9.2

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11

The number of arbitrary constants in the general solution of a differential equation of fourth order are:

As we know that the number of constant in the general solution of a differential equation of order n is equal to its order.


Thus, the number of constant in the general equation of fourth order differential equation is four.

11

Chapter Exercises

Exercise 9.1
Exercise 9.2
Exercise 9.3
Exercise 9.4
Exercise 9.5
Exercise 9.6
Miscellaneous Exercise

More Exercise Questions

1

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
2

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

y = x2 + 2x + C : y′ – 2x – 2 = 0
3

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

y = cos x + C : y′ + sin x = 0
4

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
5

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

y = Ax : xy′ = y (x ≠ 0)
6

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

y = x sin x : xy′ = y + x (x ≠ 0 and x > y or x < – y)
7

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

xy = log y + C :

8

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

y – cos y = x : (y sin y + cos y + x)y′ = y
9

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:

x + y = tan–1y : y2y′ + y2 + 1 = 0
10

In each of the question verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:
11

The number of arbitrary constants in the general solution of a differential equation of fourth order are:
12

The number of arbitrary constants in the particular solution of a differential equation of third order are: