![General solution of dy/dx = e^x+y is (a) e^x + e^-y = C [MCQ Class 12] - Ex 9.3](https://cdn.teachoo.com/757ce186-35ec-468f-88d6-42b59c11891f/slide36.jpg)
Ex 9.3, 23 (MCQ) - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Ex 9.3
Ex 9.3, 1
Important
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Transcript
Ex 9.3, 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 ∫1▒𝑒^(−𝑦) 𝑑𝑦= ∫1▒𝑒^𝑥 𝑑𝑥 〖−𝒆〗^(−𝒚) = 𝒆^𝒙+𝒄 𝑒^𝑥 + 𝑒^(−𝑦) = C So, the correct answer is (a)
