# Example 11 - Chapter 9 Class 12 Differential Equations

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 11 Find the particular solution of the differential equation 𝑑𝑦𝑑𝑥=4𝑥 𝑦2 given that 𝑦=1 , 𝑤ℎ𝑒𝑛 𝑥=0 Given differential equation , 𝑑𝑦𝑑𝑥=−4𝑥 𝑦2 𝑑𝑦 𝑦2 = (−4 x) dx Integrating both sides. 𝑑𝑦 𝑦2 = −4𝑥 𝑑𝑥 𝑑𝑦 𝑦2 = −4 𝑥 𝑑𝑥 𝑦−2+1−2+1 = −4. 𝑥22 + c 𝑦−1−1 = −2x2 + c − 1𝑦 = –2x2 + c y = −1−2𝑥2 + 𝑐 y = −1−(2𝑥2 − 𝑐) y = 12𝑥2 − 𝑐 Given that at x = 0, y = 1 Putting x = 0, y = 1, in (1) 1 = 12 02 − c 1 = 1−𝐶 c = −1 Put c = −1 in (1) y = 12 𝑥2 −(−1) y = 12 𝑥2 + 1 Hence, the particular solution of the equation is y = 𝟏𝟐 𝒙𝟐 + 𝟏

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Chapter 9 Class 12 Differential Equations

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.