Example 12 - Chapter 9 Class 12 Differential Equations (Term 2)
Last updated at Aug. 20, 2021 by Teachoo
Transcript
Example 12 Find the equation of the curve passing through the point (1 , 1) whose differential equation is ๐ฅ ๐๐ฆ= (2๐ฅ^2+1)๐๐ฅ(๐ฅโ 0) ๐ฅ ๐๐ฆ = (2x2 + 1)dx dy = "(2x2 + 1)" /๐ฅ dx dy = ("2x2" /๐ฅ+1/๐ฅ) dx dy = (2๐ฅ+1/๐ฅ) dx Integrating both sides. โซ1โ๐๐ฆ = โซ1โ(2๐ฅ+1/๐ฅ) ๐๐ฅ โซ1โ๐๐ฆ = โซ1โใ2๐ฅ ๐๐ฅ+ใ โซ1โใ1/๐ฅ ๐๐ฅใ y = 2 ๐ฅ2/2 + log |๐ฅ| + C y = ๐ฅ2 + log |๐ฅ| + C Since the curve passes through point (1, 1) Putting x = 1, y = 1 is (1) 1 = 12 + log |๐| + C 1 = 1 + 0 + C 1 โ 1 = C โด C = 0 Put C = 0 in (1) i.e y = x2 + log |๐ฅ| + C y = x2 + log |๐ฅ| + 0 y = x2 + log |๐ฅ| Hence, the equation of curve is y = x2 + log |๐|
Examples
Example 1 (i)
Example 1 (ii) Important
Example 1 (iii) Important
Example 2
Example 3 Important
Example 4 Deleted for CBSE Board 2022 Exams
Example 5 Deleted for CBSE Board 2022 Exams
Example 6 Important Deleted for CBSE Board 2022 Exams
Example 7 Deleted for CBSE Board 2022 Exams
Example 8 Deleted for CBSE Board 2022 Exams
Example 9
Example 10
Example 11
Example 12 Important You are here
Example 13
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Example 18 Important
Example 19
Example 20 Important
Example 21 Deleted for CBSE Board 2022 Exams
Example 22 Important
Example 23 Important
Example 24
Example 25 Deleted for CBSE Board 2022 Exams
Example 26
Example 27 Important
Example 28 Important Deleted for CBSE Board 2022 Exams
Chapter 9 Class 12 Differential Equations (Term 2)
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 10 years. He provides courses for Maths and Science at Teachoo.