Ex 9.4, 23 - General solution of dy/dx = ex+y is - Variable separation - Equation given

  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Ex 9.4, 23 The general solution of the differential equation 𝑑𝑦﷮𝑑𝑥﷯= 𝑒﷮𝑥+𝑦﷯ is (A) 𝑒﷮𝑥﷯+ 𝑒﷮−𝑦﷯=𝐶 (B) 𝑒﷮𝑥﷯+ 𝑒﷮𝑦﷯=𝐶 (C) 𝑒﷮−𝑥﷯+ 𝑒﷮𝑦﷯=𝐶 (D) 𝑒﷮−𝑥﷯+ 𝑒﷮−𝑦﷯=𝐶 𝑑𝑦﷮𝑑𝑥﷯ = 𝑒﷮𝑥 + 𝑦﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑒﷮𝑥 ﷯ 𝑒﷮ 𝑦﷯ 𝑑𝑦﷮ 𝑒﷮𝑦﷯﷯ = 𝑒﷮𝑥 ﷯𝑑𝑥 Integrating both sides ﷮﷮ 𝑒﷮−𝑦﷯﷯𝑑𝑦= ﷮﷮ 𝑒﷮𝑥﷯﷯𝑑𝑥 −𝑒﷮−𝑦﷯ = 𝑒﷮𝑥﷯+𝑐 𝑒﷮𝑥﷯ + 𝑒﷮−𝑦﷯ = C ∴ Option (A) is correct.

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