Ex 9.4, 8 - Find general solution: x5 dy/dx = -y5 - Variable separation - Equation given

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Ex 9.4, 8 For each of the differential equations in Exercises 1 to 10, find the general solution : 𝑥﷮5﷯ 𝑑𝑦﷮𝑑𝑥﷯=− 𝑦﷮5﷯ 𝑥﷮5﷯ 𝑑𝑦﷮𝑑𝑥﷯=− 𝑦﷮5﷯ −𝑑𝑦﷮ 𝑦﷮5﷯﷯ = −𝑑𝑥﷮ 𝑥﷮5﷯﷯ Integrating both sides − ﷮﷮ 𝑑𝑦﷮ 𝑦﷮5﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ 𝑥﷮5﷯﷯﷯ − 𝑦﷮−5 + 1﷯﷮−5 + 1﷯ = 𝑥﷮−5 + 1﷯﷮−5 + 1﷯+𝐶1 − 𝑦﷮−4﷯﷮−4﷯= 𝑥﷮−4﷯﷮−4﷯ + C1 𝑦﷮−4﷯﷮4﷯= − 𝑥﷮−4﷯﷮4﷯ + C1 𝑦﷮−4﷯ = –x-4 + 4C1 𝑦﷮−4﷯ = – 𝑥﷮−4﷯ + C 𝒙﷮−𝟒﷯ + 𝒚﷮−𝟒﷯=𝑪

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