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Ex 9.5, 16 - A homogeneous differential equation of form dx/dy = h(x/y

Ex 9.5, 16 - Chapter 9 Class 12 Differential Equations - Part 2

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Ex 9.5, 16 A homogeneous differential equation of the from 𝑑𝑥/𝑑𝑦=ℎ(𝑥/𝑦) can be solved by substitution. (A) 𝑦=𝑣𝑥 (B) 𝑣=𝑦𝑥 (C) 𝑥=𝑣𝑦 (D) 𝑥=𝑣 Given 𝑑𝑥/𝑑𝑦 = h(𝑥/𝑦) Here, h(𝑥/𝑦) is a function of 𝑥/𝑦 So, we will make the substitution x = vy ∴ (C) is the correct answer. Note: An example of function h(𝑥/𝑦) can be h(𝑥/𝑦) = (𝑒^(𝑥/𝑦)−1)/(𝑥/𝑦) So, we solve it by substituting x = vy

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