
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Ex 9.4, 5 For each of the differential equations in Exercises 1 to 10, find the general solution : 𝑒𝑥+ 𝑒−𝑥𝑑𝑦− 𝑒𝑥− 𝑒−𝑥𝑑𝑥=0 𝑒𝑥+ 𝑒−𝑥𝑑𝑦− 𝑒𝑥− 𝑒−𝑥𝑑𝑥=0 𝑒𝑥+ 𝑒−𝑥 dy = 𝑒𝑥− 𝑒−𝑥 dx 𝑑𝑦𝑑𝑥 = 𝑒𝑥 − 𝑒−𝑥 𝑒𝑥 + 𝑒−𝑥 dx 𝑑𝑦 = 𝑒𝑥 − 𝑒−𝑥 𝑒𝑥 + 𝑒−𝑥 dx Integrating both sides. 𝑑𝑦 = 𝑒𝑥 − 𝑒−𝑥 𝑒𝑥 + 𝑒−𝑥 dx 𝑦 = 𝑒𝑥 − 𝑒−𝑥 𝑒𝑥 + 𝑒−𝑥 dx Let t = 𝑒𝑥+ 𝑒−𝑥 𝑑𝑡𝑑𝑥 = 𝑒𝑥− 𝑒−𝑥 dx dx = 𝑑𝑡 𝑒𝑥 − 𝑒−𝑥 Substituting values in (1), we get 𝑑𝑦 = 𝑒𝑥 − 𝑒−𝑥𝑡 𝑑𝑡 𝑒𝑥 − 𝑒−𝑥 . 𝑑𝑦 = 𝑑𝑡𝑡 y = log 𝑡+𝑐 Putting back t = 𝑒𝑥− 𝑒−𝑥 y = log 𝑒𝑥− 𝑒−𝑥 + C y = log ( 𝒆𝒙− 𝒆−𝒙) + C
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