NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.2.
- Differential Equations Class 12 Ex 9.1
- Differential Equations Class 12 Ex 9.3
- Differential Equations Class 12 Ex 9.4
- Differential Equations Class 12 Ex 9.5
- Differential Equations Class 12 Ex 9.6
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 12 |
| Subject | Maths |
| Chapter | Chapter 9 |
| Chapter Name | Differential Equations |
| Exercise | Ex 9.2 |
| Number of Questions Solved | 12 |
| Category | NCERT Solutions |
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.
\(y=Ax:x{ y }^{ I }=y(x\neq 0)\)
Solution:
\(y=Ax:x{ y }^{ I }=y(x\neq 0)\)
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:
\(y=x\quad sinx;{ xy }^{ I }=y+x\sqrt { { x }^{ 2 }-{ y }^{ 2 } } (x\neq 0\quad and\quad x>y\quad or\quad x<-y)\)
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.
\(y=\sqrt { { a }^{ 2 }-{ x }^{ 2 } } x\in (-a,a);x+y\frac { dy }{ dx } =0,(y\neq 0)\)
Solution:
\(y=\sqrt { { a }^{ 2 }-{ x }^{ 2 } } x\in (-a,a);x+y\frac { dy }{ dx } =0,(y\neq 0)\)
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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