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

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

In mathematics, Class 12 Chapter 9 Differential Equations, a differential equation is an equation that deals with one or more functions and their derivatives. In applications, functions typically represent physical quantities, derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relationships are very common; And, differential equations play a major role in many other disciplines including engineering, physics, economics and biology.

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals  are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals.


  • 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

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

    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,
    UP Board Solutions for Class 12 Maths Chapter 9 Differential Equations 7
    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
    NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations 9.1

    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.

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