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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
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Chapter 9 Class 12 Differential Equations
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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.