Example 26 - Chapter 9 Class 12 Differential Equations
Last updated at May 29, 2018 by Teachoo
Transcript
Example 26 Find the particular solution of the differential equation log 𝑑𝑦𝑑𝑥=3𝑥+4𝑦 given that 𝑦= 𝑤ℎ𝑒𝑟𝑒 𝑥=0 log 𝑑𝑦𝑑𝑥=3𝑥+4𝑦 𝑑𝑦𝑑𝑥 = e(3x + 4y) 𝑑𝑦𝑑𝑥 = e3x e4y Separating the variables 𝑑𝑦 𝑒4𝑦 = e3x dx Integrating both sides. 𝑒−4𝑦 𝑑𝑦= 𝑒3𝑥 𝑑𝑥 𝑒−4𝑦4 = 𝑒3𝑥3 + C 𝑒3𝑥3 + 𝑒−4𝑦4 = C 4𝑒3𝑥 + 3 𝑒−4𝑦12 + 12C = 0 4 𝑒3𝑥 + 3 𝑒−4𝑦 + 12C = 0 Given y = 0 when x = 0 Putting x = 0 & y = 0 in (1) 4 𝑒3(0) + 3 𝑒−4(0) + 12C = 0 4 𝑒(0) + 3 𝑒(0) + 12C = 0 4 + 3 + 12C = 0 12C = – 7 C = −712 Putting value of C in (1) 4 𝑒3𝑥 + 3 𝑒−4𝑦 + 12C = 0 4 𝑒3𝑥 + 3 𝑒−4𝑦 + 12 −712 = 0 𝟒 𝒆−𝟑𝒙 + 𝟑 𝒆−𝟒𝒚 − 7 = 0
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Chapter 9 Class 12 Differential Equations
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.