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

Get Free NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Differential Equations Exercise 9.2 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 9 Class 12 Differential Equations Ex 9.2 provided in NCERT Textbook.

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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:
$y={ e }^{ x }+1:{ y }^{ II }-{ y }^{ I }=0$
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 1

Ex 9.2 Class 12 Maths Question 2.
$y=x^{ 2 }+2x+c:{ y }^{ I }-2x-2=0$
Solution:
$y=x^{ 2 }+2x+c:{ y }^{ I }-2x-2=0$
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 2

Ex 9.2 Class 12 Maths Question 3.
$y=cosx+c:{ y }^{ I }+sinx=0$
Solution:
$y=cosx+c:{ y }^{ I }+sinx=0$
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 3

Ex 9.2 Class 12 Maths Question 4.
$y=\sqrt { 1+{ x }^{ 2 } } :{ y }^{ I }=\frac { xy }{ 1+{ x }^{ 2 } }$
Solution:
$y=\sqrt { 1+{ x }^{ 2 } } :{ y }^{ I }=\frac { xy }{ 1+{ x }^{ 2 } }$
vedantu class 12 maths Chapter 9 Differential Equations 4

Ex 9.2 Class 12 Maths Question 5.
$y=Ax:x{ y }^{ I }=y(x\neq 0)$
Solution:
$y=Ax:x{ y }^{ I }=y(x\neq 0)$
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 5

Ex 9.2 Class 12 Maths Question 6.
$y=x\quad sinx;{ xy }^{ I }=y+x\sqrt { { x }^{ 2 }-{ y }^{ 2 } } (x\neq 0\quad and\quad x>y\quad or\quad x<-y)$
Solution:
$y=x\quad sinx;{ xy }^{ I }=y+x\sqrt { { x }^{ 2 }-{ y }^{ 2 } } (x\neq 0\quad and\quad x>y\quad or\quad x<-y)$
NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 6

Ex 9.2 Class 12 Maths Question 7.
xy = logy + C,
UP Board Solutions for Class 12 Maths Chapter 9 Differential Equations 7
Solution:
xy = logy + C,

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 7

Ex 9.2 Class 12 Maths Question 8.
$y-cosy=x:(ysiny+cosy+x){ y }^{ I }=y$
Solution:
$y-cosy=x:(ysiny+cosy+x){ y }^{ I }=y$
vedantu class 12 maths Chapter 9 Differential Equations 8

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

Ex 9.2 Class 12 Maths Question 10.
$y=\sqrt { { a }^{ 2 }-{ x }^{ 2 } } x\in (-a,a);x+y\frac { dy }{ dx } =0,(y\neq 0)$
Solution:
$y=\sqrt { { a }^{ 2 }-{ x }^{ 2 } } x\in (-a,a);x+y\frac { dy }{ dx } =0,(y\neq 0)$
vedantu class 12 maths Chapter 9 Differential Equations 10

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.