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Prévia do material em texto
𝒅𝒙 𝒅𝒕 = 𝒕𝒙² 𝑑𝑥 𝑑𝑡 = 0. 𝑑𝑥 𝑑𝑡 = 𝑡𝑥² 𝑑𝑥 𝑑𝑡 = 0 𝑡𝑥2 = 0 𝑡𝑥2 𝑡 = 0 𝑡 𝑥2 = 0 → 𝑥 = ±√0 = 0 𝑥(𝑡) = 0. 𝑑𝑥 𝑑𝑡 = 𝑥2 − 𝑥 𝑑𝑥 𝑑𝑡 = 0. 𝑑𝑥 𝑑𝑡 = 𝑥2 − 𝑥 𝑑𝑥 𝑑𝑡 = 0 𝑥2 − 𝑥 = 0 𝑥 = 0 𝑥 − 1 = 0 → 𝑥 = 1 𝑥(𝑡) = 0 𝑜𝑢 𝑥(𝑡) = 1. 𝑑𝑥 𝑑𝑡 = 𝑡(1 + 𝑥2) 𝑑𝑥 𝑑𝑡 = 0. 𝑑𝑥 𝑑𝑡 = 𝑡(1 + 𝑥2) 𝑑𝑥 𝑑𝑡 = 0 𝑡(1 + 𝑥2) = 0 𝑡(1+𝑥2) 𝑡 = 0 𝑡 1 + 𝑥2 = 0 → 𝑥2 = −1 → 𝑥 = √−1 𝑑𝑥 𝑑𝑡 = 𝑡 𝑥 𝑑𝑥 𝑑𝑡 = 0. 𝑑𝑥 𝑑𝑡 = 𝑡 𝑥 𝑑𝑥 𝑑𝑡 = 0 𝑡 𝑥 = 0 𝑡 𝑥 ∙ 𝑥 = 0 ∙ 𝑥 𝑡 = 0 𝑑𝑥 𝑑𝑡 = 𝑡2−1 𝑥 𝑑𝑥 𝑑𝑡 = 0. 𝑑𝑥 𝑑𝑡 = 𝑡2−1 𝑥 𝑑𝑥 𝑑𝑡 = 0 𝑡2−1 𝑥 = 0 𝑡2−1 𝑥 ∙ 𝑥 = 0 ∙ 𝑥 𝑡2 − 1 = 0 → 𝑡2 = 1 𝑑𝑥 𝑑𝑡 = 𝑥2−1 𝑡 , 𝑡 < 0 𝑑𝑥 𝑑𝑡 = 0. 𝑑𝑥 𝑑𝑡 = 𝑥²−1 𝑡 𝑑𝑥 𝑑𝑡 = 0 𝑥2−1 𝑡 = 0 𝑥2−1 𝑡 ∙ 𝑡 = 0 ∙ 𝑡 𝑥2 − 1 = 0 → 𝑥1 = 1 → 𝑥 = ±√1 = ±1 𝑥(𝑡) = 1 𝑜𝑢 𝑥(𝑡) = −1.
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