LORENA LARA BARRAZA
ITA 801
2° PARCIAL
1. 𝑑𝑦
𝑑𝑥 =𝑆𝑒𝑛 5𝑥 − −→ 𝐷𝑒𝑠𝑝𝑒𝑗𝑎𝑚𝑜𝑠 𝑑𝑦 =𝑆𝑒𝑛 5𝑥 𝑑𝑥
∫𝑑𝑦 = ∫𝑆𝑒𝑛 (5𝑥)𝑑𝑥 hacemos cambio de variable 𝑢 = 5𝑥−→ 𝑑𝑢 = 5𝑑𝑥
∫𝑆𝑒𝑛 𝑢 𝑑𝑢 − −→ ∫ 𝑆𝑒𝑛 (5𝑥)5𝑑𝑥− −→ 1
5∫𝑆𝑒𝑛 5𝑥 5𝑑𝑥
𝑦 = −1
5𝐶𝑜𝑠 5𝑥 + 𝐶
2. 𝑑𝑦
𝑑𝑥 = 𝑒3𝑥+2𝑦 − − → 𝑑𝑦
𝑑𝑥 = 𝑒3𝑥 𝑒2𝑦 − −→ 𝐷𝑒𝑠𝑝𝑒𝑗𝑎𝑚𝑜𝑠 1
𝑒2𝑦 𝑑𝑦 = 𝑒3𝑥𝑑𝑥
∫𝑒−2𝑦𝑑𝑦 = ∫𝑒3𝑥𝑑𝑥
−1
2∫𝑒−2𝑦(−2)𝑑𝑦 =1
3∫𝑒3𝑥(3)𝑑𝑥 + 𝐶 − −→ 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑖𝑐𝑎𝑚𝑜𝑠 𝑑𝑖𝑣𝑖𝑑𝑖𝑒𝑛𝑑𝑜 𝑒𝑛𝑡𝑟𝑒 2.
𝑒−2𝑦 = −2
3𝑒3𝑥 + 𝐶 𝑆𝑜𝑙𝑛 𝑖𝑛𝑝𝑙𝑖𝑐𝑖𝑡𝑎
𝐼𝑛𝑒−2𝑦 =𝐼𝑛(−2
3𝑒3𝑥 + 𝐶) − −→ −2𝑦 = 𝐼𝑛(−2
3𝑒3𝑥 +𝐶)
𝑦 = 𝐼𝑛(−2
3𝑒3𝑥 +𝐶)
2
