Check sibling questions

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


Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.