# Example 11

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 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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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.