CBSE Class 12 Sample Paper for 2020 Boards
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CBSE Class 12 Sample Paper for 2020 Boards
Last updated at April 16, 2024 by Teachoo
Question 20 Write the general solution of differential equation 𝑑𝑦/𝑑𝑥 = 𝑒^(𝑥+𝑦) Given 𝑑𝑦/𝑑𝑥 = 𝑒^(𝑥+𝑦) 𝑑𝑦/𝑑𝑥 = 𝑒^𝑥.𝑒^𝑦 𝑑𝑦/𝑒^𝑦 = 𝑒^𝑥 𝑑𝑥 e^(−𝑦) 𝑑𝑦 = 𝑒^𝑥 𝑑𝑥 Integrating both sides ∫1▒〖e^(−𝑦) 𝑑𝑦〗 = ∫1▒〖𝑒^𝑥 𝑑𝑥" " 〗 −𝑒^(−𝑦) = 𝑒^𝑥+𝑐 0 = 𝑒^𝑥+𝑒^(−𝑦)+ C Or we can write it as 𝒆^𝒙+𝒆^(−𝒚)= C Thus, the general solution is 𝒆^𝒙+𝒆^(−𝒚)= C
