Request a call back

Join NOW to get access to exclusive study material for best results

Class 12-commerce NCERT Solutions Maths Chapter 9 - Differential Equations

Differential Equations Exercise Ex. 9.1

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Differential Equations Exercise Ex. 9.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Differential Equations Exercise Ex. 9.3

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Let x and y be the x-coordinate and y-coordinate of the point on the curve respectively.

We know that the slope of a tangent to the curve in the coordinate axes is given by the relation,

 

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

..

Solution 23

Differential Equations Exercise Ex. 9.4

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Differential Equations Exercise Ex. 9.5

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Differential Equations Exercise Misc. Ex.

Solution 1

Solution 2

begin mathsize 14px style left parenthesis straight i right parenthesis space
x y equals a e to the power of x plus b e to the power of negative x end exponent plus x squared
Differentiating space both space sides space straight w. straight r. straight t space x space we space get
fraction numerator d left parenthesis x y right parenthesis over denominator d x end fraction equals a fraction numerator d over denominator d x end fraction open parentheses e to the power of x close parentheses plus b fraction numerator d over denominator d x end fraction open parentheses e to the power of negative x end exponent close parentheses plus fraction numerator d over denominator d x end fraction left parenthesis 2 x right parenthesis
rightwards double arrow x fraction numerator d y over denominator d x end fraction plus y equals a e to the power of x minus b e to the power of negative x end exponent plus 2 x
Again comma space differentiating space both space the space sides space straight w. straight r. straight t. space x comma space we space get
x fraction numerator d squared y over denominator d x squared end fraction plus fraction numerator d y over denominator d x end fraction plus fraction numerator d y over denominator d x end fraction equals a fraction numerator d over denominator d x end fraction left parenthesis e to the power of x right parenthesis minus b fraction numerator d over denominator d x end fraction left parenthesis e to the power of negative x end exponent right parenthesis plus 2 fraction numerator d over denominator d x end fraction left parenthesis x right parenthesis
rightwards double arrow x fraction numerator d squared y over denominator d x squared end fraction plus 2 fraction numerator d y over denominator d x end fraction equals a e to the power of x plus b e to the power of negative x end exponent plus 2
rightwards double arrow x fraction numerator d squared y over denominator d x squared end fraction plus 2 fraction numerator d y over denominator d x end fraction equals x y minus x squared plus 2
rightwards double arrow x fraction numerator d squared y over denominator d x squared end fraction plus 2 fraction numerator d y over denominator d x end fraction minus x y plus x squared minus 2 equals 0
Hence comma space the space given space function space is space straight a space solution space of space the space corresponding space differential space equation. end style

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Get Latest Study Material for Academic year 24-25 Click here
×