# NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2

In this chapter, we provide NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 pdf, free NCERT solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 book pdf download.

## NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation

Ex 9.2 Class 12 Maths Question 1.
$y={ e }^{ x }+1:{ y }^{ II }-{ y }^{ I }=0$
Solution:
$y={ e }^{ x }+1:{ y }^{ II }-{ y }^{ I }=0$

Ex 9.2 Class 12 Maths Question 2.
$y=x^{ 2 }+2x+c:{ y }^{ I }-2x-2=0$
Solution:
$y=x^{ 2 }+2x+c:{ y }^{ I }-2x-2=0$

Ex 9.2 Class 12 Maths Question 3.
$y=cosx+c:{ y }^{ I }+sinx=0$
Solution:
$y=cosx+c:{ y }^{ I }+sinx=0$

Ex 9.2 Class 12 Maths Question 4.
$y=sqrt { 1+{ x }^{ 2 } } :{ y }^{ I }=frac { xy }{ 1+{ x }^{ 2 } }$
Solution:
$y=sqrt { 1+{ x }^{ 2 } } :{ y }^{ I }=frac { xy }{ 1+{ x }^{ 2 } }$

Ex 9.2 Class 12 Maths Question 5.
$y=Ax:x{ y }^{ I }=y(xneq 0)$
Solution:
$y=Ax:x{ y }^{ I }=y(xneq 0)$

Ex 9.2 Class 12 Maths Question 6.
$y=xquad sinx;{ xy }^{ I }=y+xsqrt { { x }^{ 2 }-{ y }^{ 2 } } (xneq 0quad andquad x>yquad orquad x<-y)$
Solution:
$y=xquad sinx;{ xy }^{ I }=y+xsqrt { { x }^{ 2 }-{ y }^{ 2 } } (xneq 0quad andquad x>yquad orquad x<-y)$

Ex 9.2 Class 12 Maths Question 7.
xy = logy + C,

Solution:
xy = logy + C,

Ex 9.2 Class 12 Maths Question 8.
$y-cosy=x:(ysiny+cosy+x){ y }^{ I }=y$
Solution:
$y-cosy=x:(ysiny+cosy+x){ y }^{ I }=y$

Ex 9.2 Class 12 Maths Question 9.
$x+y={ ta }n^{ -1 }y;{ y }^{ 2 }{ y }^{ I }+{ y }^{ 2 }+1=0$
Solution:
$x+y={ ta }n^{ -1 }y;{ y }^{ 2 }{ y }^{ I }+{ y }^{ 2 }+1=0$

Ex 9.2 Class 12 Maths Question 10.
$y=sqrt { { a }^{ 2 }-{ x }^{ 2 } } xin (-a,a);x+yfrac { dy }{ dx } =0,(yneq 0)$
Solution:
$y=sqrt { { a }^{ 2 }-{ x }^{ 2 } } xin (-a,a);x+yfrac { dy }{ dx } =0,(yneq 0)$

Ex 9.2 Class 12 Maths Question 11.
The number of arbitrary constants in the general solution of a differential equation of fourth order are:
(a) 0
(b) 2
(c) 3
(d) 4
Solution:
(b) The general solution of a differential equation of fourth order has 4 arbitrary constants.
Because it contains the same number of arbitrary constants as the order of differential equation.

Ex 9.2 Class 12 Maths Question 12.
The number of arbitrary constants in the particular solution of a differential equation of third order are:
(a) 3
(b) 2
(c) 1
(d) 0
Solution:
(d) Number of arbitrary constants = 0
Because particular solution is free from arbitrary constants.

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