# Example 22

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 22 Find the particular solution of the differential equation / + cot =2 + ^2 cot ( 0) given that =0 = /2 / + cot =2 + ^2 cot Differential equation is of the form / + = where P = cot x & Q = 2x + x2 cot x IF = ^ 1 IF = ^ 1 cot IF = ^"log sin x " IF = sin x Solution is y (IF) = 1 ( ) + y sin x 1 sin =(2 + ^(2 ) cot ) + y sin x = 1 (2 sin + ^(2 ) sin cot ) + y sin = 1 2 sin + 1 ^2 sin cot + y sin = 2 1 sin ( ) + ^2 sin cot + y sin = 2 [sin 1 1 [cos 1 ] ] + 1 ^2 sin cos /sin dx + C y sin x = 2 sin x ["sin x " [ ^2/2]" 2" 1 cos x [ ^2/2] + 1 ^2 cos " dx + c" ] y sin x = x2sin x 1 ^2 cos x dx + 1 ^2 cos x dx + c y sin x = x2 sin x + c Given that y = 0 when x = /2 Putting = /2 and y = 0 in (1) (0) sin /2=( /2)^2 sin ( /2)+C 0 = ^2/4 (1)+C ^2/4=C Putting value in C in (1) y sin x = ^2 sin ^2/4 Dividing whole by sin x ( sin )/sin =( ^2 sin )/sin ^2/(4 sin ) = ^ ^ /

Chapter 9 Class 12 Differential Equations

Example 1
Important

Ex 9.1, 11 Important

Ex 9.1, 12 Important

Example 7 Important

Ex 9.3, 7 Important

Ex 9.3, 10 Important

Example 13 Important

Ex 9.4, 14 Important

Example 17 Important

Example 18 Important

Ex 9.5, 8 Important

Ex 9.5, 15 Important

Example 22 Important You are here

Ex 9.6, 7 Important

Ex 9.6, 13 Important

Ex 9.6, 14 Important

Example 25 Important

Example 27 Important

Example 28 Important

Misc 6 Important

Misc 11 Important

Misc 12 Important

Misc 13 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.