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Example 11 - Find particular solution: dy/dx = 4xy2 - Examples

Example 11 - Chapter 9 Class 12 Differential Equations - Part 2
Example 11 - Chapter 9 Class 12 Differential Equations - Part 3

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Example 11 Find the particular solution of the differential equation 𝑑𝑦/𝑑π‘₯=βˆ’4π‘₯𝑦^2 given that 𝑦=1 , π‘€β„Žπ‘’π‘› π‘₯=0 Given differential equation , 𝑑𝑦/𝑑π‘₯=βˆ’4π‘₯𝑦^2 𝑑𝑦/𝑦^2 = (βˆ’4 x) dx Integrating both sides. ∫1▒𝑑𝑦/𝑦^2 = ∫1β–’γ€–βˆ’4π‘₯ 𝑑π‘₯γ€— ∫1▒𝑑𝑦/𝑦^2 = βˆ’4 ∫1β–’γ€–π‘₯ 𝑑π‘₯γ€— 𝑦^(βˆ’2+1)/(βˆ’2+1) = βˆ’4.π‘₯^2/2 + c 𝑦^(βˆ’1)/(βˆ’1) = βˆ’2x2 + c βˆ’ 1/𝑦 = –2x2 + c y = (βˆ’1)/(βˆ’2π‘₯2 + 𝑐) y = (βˆ’1)/(βˆ’(2π‘₯2 βˆ’ 𝑐)) y = 1/(2π‘₯2 βˆ’ 𝑐) Given that at x = 0, y = 1 Putting x = 0, y = 1, in (1) 1 = 1/(2(0)^2 ) βˆ’ c 1 = 1/(βˆ’πΆ) c = βˆ’1 Put c = βˆ’1 in (1) y = 1/(2π‘₯^2 ) βˆ’(βˆ’1) y = 1/(2π‘₯^2 + 1) Hence, the particular solution of the equation is y = 𝟏/(πŸπ’™^𝟐 + 𝟏)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.