Example 26 - Find particular solution log (dy/dx) =3x + 4y - Examples

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Slide26.JPG

  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Example 26 Find the particular solution of the differential equation log 𝑑𝑦﷮𝑑𝑥﷯﷯=3𝑥+4𝑦 given that 𝑦= 𝑤ℎ𝑒𝑟𝑒 𝑥=0 log 𝑑𝑦﷮𝑑𝑥﷯﷯=3𝑥+4𝑦 𝑑𝑦﷮𝑑𝑥﷯ = e(3x + 4y) 𝑑𝑦﷮𝑑𝑥﷯ = e3x e4y Separating the variables 𝑑𝑦﷮ 𝑒﷮4𝑦﷯﷯ = e3x dx Integrating both sides. ﷮﷮ 𝑒﷮−4𝑦﷯ 𝑑𝑦=﷯ ﷮﷮ 𝑒﷮3𝑥﷯ 𝑑𝑥﷯ 𝑒﷮−4𝑦﷯﷮4﷯ = 𝑒﷮3𝑥﷯﷮3﷯ + C 𝑒﷮3𝑥﷯﷮3﷯ + 𝑒﷮−4𝑦﷯﷮4﷯ = C 4𝑒3𝑥 + 3 𝑒﷮−4𝑦﷯﷮12﷯ + 12C = 0 4 𝑒﷮3𝑥﷯ + 3 𝑒﷮−4𝑦﷯ + 12C = 0 Given y = 0 when x = 0 Putting x = 0 & y = 0 in (1) 4 𝑒﷮3(0)﷯ + 3 𝑒﷮−4(0)﷯ + 12C = 0 4 𝑒﷮(0)﷯ + 3 𝑒﷮(0)﷯ + 12C = 0 4 + 3 + 12C = 0 12C = – 7 C = −7﷮12﷯ Putting value of C in (1) 4 𝑒﷮3𝑥﷯ + 3 𝑒﷮−4𝑦﷯ + 12C = 0 4 𝑒﷮3𝑥﷯ + 3 𝑒﷮−4𝑦﷯ + 12 −7﷮12﷯﷯ = 0 𝟒 𝒆﷮−𝟑𝒙﷯ + 𝟑 𝒆﷮−𝟒𝒚﷯ − 7 = 0

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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.