8. 𝑒 𝑥 𝑦 𝑒𝑥𝑦 𝑑𝑦 𝑑𝑥 = 𝑒 −𝑦 + 𝑒 −2𝑥−𝑦 𝑑𝑦 = 𝑒 −𝑦 (1 + 𝑒 −2𝑥 ) 𝑑𝑥 𝑒 𝑥 𝑦 𝑑𝑦 = 𝑒 −𝑦 (1 + 𝑒 −2𝑥 ) 𝑑𝑥 𝑦 𝑑𝑦 1 + 𝑒 −2𝑥 =( )𝑑𝑥 𝑒 −𝑦 𝑒𝑥 𝑦 𝑒 𝑦 𝑑𝑦 = (𝑒 −𝑥 + 𝑒 −3𝑥 ) 𝑑𝑥 ∫ 𝑦 𝑒 𝑦 𝑑𝑦 = ∫(𝑒 −𝑥 + 𝑒 −3𝑥 ) 𝑑𝑥 = 𝑒 𝑦 (𝑦 − 1) = −𝑒 −𝑥 − 1 3 𝑒 −3𝑥 + 𝑐
8. 𝑒 𝑥 𝑦 𝑒𝑥𝑦 𝑑𝑦 𝑑𝑥 = 𝑒 −𝑦 + 𝑒 −2𝑥−𝑦 𝑑𝑦 = 𝑒 −𝑦 (1 + 𝑒 −2𝑥 ) 𝑑𝑥 𝑒 𝑥 𝑦 𝑑𝑦 = 𝑒 −𝑦 (1 + 𝑒 −2𝑥 ) 𝑑𝑥 𝑦 𝑑𝑦 1 + 𝑒 −2𝑥 =( )𝑑𝑥 𝑒 −𝑦 𝑒𝑥 𝑦 𝑒 𝑦 𝑑𝑦 = (𝑒 −𝑥 + 𝑒 −3𝑥 ) 𝑑𝑥 ∫ 𝑦 𝑒 𝑦 𝑑𝑦 = ∫(𝑒 −𝑥 + 𝑒 −3𝑥 ) 𝑑𝑥 = 𝑒 𝑦 (𝑦 − 1) = −𝑒 −𝑥 − 1 3 𝑒 −3𝑥 + 𝑐