Example 6 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 6 Find the particular solution of the differential equation ๐๐ฆ/๐๐ฅ=โ4๐ฅ๐ฆ^2 given that ๐ฆ=1 , ๐คโ๐๐ ๐ฅ=0Given differential equation , ๐๐ฆ/๐๐ฅ=โ4๐ฅ๐ฆ^2 ๐ ๐/๐^๐ = (โ4 x) dx Integrating both sides. โซ1โ๐๐ฆ/๐ฆ^2 = โซ1โใโ4๐ฅ ๐๐ฅใ โซ1โ๐ ๐/๐^๐ = โ4 โซ1โใ๐ ๐ ๐ใ ๐ฆ^(โ2+1)/(โ2+1) = โ4.๐ฅ^2/2 + c โ ๐/๐ = โ2x2 + c y = (โ1)/(โ2๐ฅ2 + ๐) y = (โ1)/(โ(2๐ฅ2 โ ๐)) y = ๐/(๐๐๐ 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 Putting c = โ1 in (1) y = 1/(2๐ฅ^2 ) โ(โ1) y = ๐/(๐๐^๐ + ๐) Hence, the particular solution of the equation is y = ๐/(๐๐^๐ + ๐)
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo