Example 27 - Chapter 9 Class 12 Differential Equations
Last updated at May 29, 2018 by Teachoo
Transcript
Example 27 Solve 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
Examples
Example 1
Important
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7 Important
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13 Important
Example 14
Example 15
Example 16
Example 17 Important
Example 18 Important
Example 19
Example 20
Example 21
Example 22 Important
Example 23
Example 24
Example 25 Important
Example 26
Example 27 Important You are here
Example 28 Important
Chapter 9 Class 12 Differential Equations
Serial order wise
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.