# Example 27

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 27Solve the differential equation ( ) ( / )=( + ) cos ( / ) ( ) ( / )=( + ) cos ( / ) sin ( / ) ^2 ( / ) = cos ( / ) + ^2 cos ( / ) [ sin ( / ) ^2 ( / ) ] =[ cos ( / )+ ^2 sin ( / ) ] / = ( cos ( / ) + ^2 sin ( / ) )/( sin ( / ) ^2 ( / ) ) Dividing numerator & denominator by x2 / = ( / cos ( / ) + ( / )^2 cos ( / ) )/( / sin ( / ) cos ( / ) ) Let y = vx / = v + / Putting value of / and y in (1) v + ( )/ =( / cos ( / ) + ( ^2 ^2)/ ^2 sin ( / ) )/( / sin ( / ) ( / ) ) v + ( )/ = ( cos + ^2 sin )/( sin cos ) x ( )/ = ( cos + ^2 sin )/( sin cos ) v x ( )/ = ( cos + ^2 sin ( sin cos ) )/( sin cos ) x ( )/ = ( cos + ^2 sin ^2 sin + cos )/( sin cos ) ( )/ = (2 cos )/( sin cos ) (( sin cos )/ v cos ) =2 / (( sin )/ v cos cos / v cos ) dv = 2 / (tan 1/ ) dv = 2 / Integrating both sides 1 (tan 1/ ) =2 1 / 1 tan 1 / = 2 1 / log |sec | | | = 2 log | | + log| | sec ( / ) = C xy

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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

Ex 9.6, 7 Important

Ex 9.6, 13 Important

Ex 9.6, 14 Important

Example 25 Important

Example 27 Important You are here

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.