In this page we have *NCERT Solutions for Class 12 Maths Chapter 9: Differential Equations* for
EXERCISE 9.2 . Hope you like them and do not forget to like , social share
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y= e

Differentiating both sides of this equation with respect to x, we get:

y

Now, differentiating equation (1) with respect to x, we get:

y

Substituting the values of in the given differential equation, we get the L.H.S.

as:

e

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

y=x

Differentiating both sides of this equation with respect to x, we get:

(dy/dx) = 2x +2

Substituting the value in the given differential equation, we get:

L.H.S. =

(dy/dx) -2x -2 =0

=(2x+2) -2x-2=0

= R.H.S.

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

y= cos x + C : (dy/dx) +sin x =0

Differentiating both sides of this equation with respect to x, we get:

(dy/dx) = -sin x

Substituting the value in the given differential equation, we get:

L.H.S. =

(dy/dx) +sin x

=-sin x + sin x

=0

= R.H.S.

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

Differentiating both sides of the equation with respect to x, we get:

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

Differentiating both sides with respect to x, we get:

dy/dx = A

Substituting the value of in the given differential equation, we get:

LHS

=x(dy/dx)

=Ax

=y

=RHS

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

Differentiating both sides of this equation with respect to x, we get:

dy/dx = sin x + x cos x

Substituting the value in the given differential equation, we get:

LHS

=x(dy/dx)

= x(sin x + x cos x)

=x sin (x) + x

Now we know that

cos

cos (x) = √( 1 – sin

Now we know that

y=x sin x or sin (x) = y/x

Therefore

cos (x) = √[ 1 –(y/x)

Substituting the value from (2) in (1)

=x sin (x) + x

= y + x √(x

=RHS

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

xy= log y + c : dy/dx = y

Differentiating both sides of this equation with respect to x, we get:

y +x (dy/dx) = (1/y) (dy/dx)

y

or

dy/dx = y

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

Differentiating both sides of the equation with respect to x, we get:

(dy/dx) + sin y (dy/dx) =1

Or

dy/dx= 1/(1+sin y)

Substituting the value of in differential equation

LHS

=(

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

x + y= tan

Differentiating both sides of this equation with respect to x, we get:

1 + (dy/dx) = [1/(1+y

1+ y

Or

y

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

y=√(a

Differentiating both sides of this equation with respect to x, we get:

Now y=√(a

So

x + y(dy/dx) =0

So, 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.

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.

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