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)

Go Ad-free
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.