Mathematics Part-II

Book: Mathematics Part-II

Chapter: 9. Differential Equations

Subject: Maths - Class 12th

Q. No. 1 of Exercise 9.2

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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

It is given that y = ex + 1

Now, differentiating both sides w.r.t. x, we get,



Now, Again, differentiating both sides w.r.t. x, we get,



⇒ y” = ex


Now, Substituting the values of y’ and y” in the given differential equations, we get,


y” – y’ = ex - ex = RHS.


Therefore, the given function is the solution of the corresponding differential equation.


1

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: