# Example 26 - Chapter 9 Class 12 Differential Equations (Term 2)

Last updated at Dec. 11, 2019 by Teachoo

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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Example 4 Deleted for CBSE Board 2022 Exams

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Example 26 You are here

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Example 28 Important Deleted for CBSE Board 2022 Exams

Chapter 9 Class 12 Differential Equations (Term 2)

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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.