Example 26 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 11, 2019 by Teachoo
Transcript
Example 26 Find the particular solution of the differential equation log(๐๐ฆ/๐๐ฅ)=3๐ฅ+4๐ฆ given that ๐ฆ=0 ๐คโ๐๐ ๐ฅ=0 log(๐๐ฆ/๐๐ฅ)=3๐ฅ+4๐ฆ ๐๐ฆ/๐๐ฅ = e(3x + 4y) ๐๐ฆ/๐๐ฅ = e3x e4y Separating the variables ๐๐ฆ/๐^4๐ฆ = e3x dx eโ4y dy = e3x dx Integrating both sides โซ1โใ๐^(โ4๐ฆ) ๐๐ฆใ=โซ1โ๐^3๐ฅ ๐๐ฅ ๐^(โ4๐ฆ)/(โ4)=๐^3๐ฅ/3+๐ถ 0=๐^3๐ฅ/3+๐^(โ4๐ฆ)/4+๐ถ ๐^3๐ฅ/3 + ๐^(โ4๐ฆ)/4 + C = 0 (4๐3๐ฅ" + " 3๐^(โ4๐ฆ))/12 + C = 0 (4๐3๐ฅ" + " 3๐^(โ4๐ฆ) + 12๐ถ)/12 " = 0" 4๐^3๐ฅ + 3๐^(โ4๐ฆ) + 12C = 0 Given y = 0 when x = 0 โฆ(1) Putting x = 0 & y = 0 in (1) 4๐^(3(0)) + 3๐^(โ4(0)) + 12C = 0 4๐^0 + 3๐^0 + 12C = 0 4 + 3 + 12C = 0 7 + 12C = 0 12C = โ 7 C = (โ7)/12 Putting value of C in (1) 4๐^3๐ฅ + 3๐^(โ4๐ฆ) + 12C = 0 4๐^3๐ฅ + 3๐^(โ4๐ฆ) + 12((โ7)/12) = 0 ๐๐^๐๐ + ๐๐^(โ๐๐) โ 7 = 0
Examples
Example 1
Important
Example 2
Example 3
Example 4
Example 5
Example 6 Important
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Example 18
Example 19
Example 20
Example 21
Example 22 Important
Example 23 Important
Example 24
Example 25
Example 26 You are here
Example 27 Important
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.