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Ex 9.4, 23 - General solution of dy/dx = e^x+y is (a) e^x + e^-y = C

Ex 9.4, 23 - Chapter 9 Class 12 Differential Equations - Part 2

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Ex 9.4, 23 The general solution of the differential equation 𝑑𝑦/𝑑π‘₯=𝑒^(π‘₯+𝑦) is (A) 𝑒^π‘₯+𝑒^(βˆ’π‘¦)=𝐢 (B) 𝑒^π‘₯+𝑒^𝑦=𝐢 (C) 𝑒^(βˆ’π‘₯)+𝑒^𝑦=𝐢 (D) 𝑒^(βˆ’π‘₯)+𝑒^(βˆ’π‘¦)=𝐢 𝑑𝑦/𝑑π‘₯ = 𝑒^(π‘₯ + 𝑦) 𝑑𝑦/𝑑π‘₯ = 𝑒^(π‘₯ ) 𝑒^( 𝑦) 𝑑𝑦/𝑒^𝑦 = 𝑒^(π‘₯ ) 𝑑π‘₯ Integrating both sides ∫1▒𝑒^(βˆ’π‘¦) 𝑑𝑦= ∫1▒𝑒^π‘₯ 𝑑π‘₯ γ€–βˆ’π‘’γ€—^(βˆ’π‘¦) = 𝑒^π‘₯+𝑐 𝑒^π‘₯ + 𝑒^(βˆ’π‘¦) = C ∴ Option (A) is correct.

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