# Example 11 - Chapter 9 Class 12 Differential Equations

Last updated at Dec. 24, 2018 by Teachoo

Last updated at Dec. 24, 2018 by Teachoo

Transcript

Example 11 Find the particular solution of the differential equation ๐๐ฆ/๐๐ฅ=โ4๐ฅ๐ฆ^2 given that ๐ฆ=1 , ๐คโ๐๐ ๐ฅ=0 Given differential equation , ๐๐ฆ/๐๐ฅ=โ4๐ฅ๐ฆ^2 ๐๐ฆ/๐ฆ^2 = (โ4 x) dx Integrating both sides. โซ1โ๐๐ฆ/๐ฆ^2 = โซ1โใโ4๐ฅ ๐๐ฅใ โซ1โ๐๐ฆ/๐ฆ^2 = โ4 โซ1โใ๐ฅ ๐๐ฅใ ๐ฆ^(โ2+1)/(โ2+1) = โ4.๐ฅ^2/2 + c ๐ฆ^(โ1)/(โ1) = โ2x2 + c โ 1/๐ฆ = โ2x2 + c y = (โ1)/(โ2๐ฅ2 + ๐) y = (โ1)/(โ(2๐ฅ2 โ ๐)) y = 1/(2๐ฅ2 โ ๐) Given that at x = 0, y = 1 Putting x = 0, y = 1, in (1) 1 = 1/(2(0)^2 ) โ c 1 = 1/(โ๐ถ) c = โ1 Put c = โ1 in (1) y = 1/(2๐ฅ^2 ) โ(โ1) y = 1/(2๐ฅ^2 + 1) Hence, the particular solution of the equation is y = ๐/(๐๐^๐ + ๐)

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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 10 years. He provides courses for Maths and Science at Teachoo.