математика 3

102. 𝐷 = 𝐷1 ∪ 𝐷2 bo’lsa, ikki karrali integral xossasi to’g’ri berilgan javobni toping. Найти правильное свойство двойного интеграла, если 𝐷 = 𝐷1 ∪ 𝐷2. Find correct double integral property if 𝐷 = 𝐷1 ∪ 𝐷2.

• ∬𝐷 (𝑓(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = ∬𝐷

  𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦 + ∬𝐷

  𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦

• ∬𝐷 (𝑓(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = ∬𝐷 𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦 − ∬𝐷

• ∬𝐷 (𝑓(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = ∬𝐷 𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦 ± ∬𝐷

  𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦

  𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦

  1

• ∬𝐷 (𝑓(𝑥; 𝑦))𝑑𝑥𝑑𝑦 = − ∬𝐷

  2

  𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦 + ∬𝐷 𝑓(𝑥; 𝑦)𝑑𝑥𝑑𝑦

𝑦 = 2𝑥𝑦´ + 𝑙𝑛𝑦´ Lagranj tenglamasini yeching. Решите уравнение Лагранжа

𝑦 = 2𝑥𝑦´ + 𝑙𝑛𝑦´. Solve Lagrange equation 𝑦 = 2𝑥𝑦´ + 𝑙𝑛𝑦´.

1 𝐶

• 𝑥 = − 𝑝 + 𝑝2

  𝑦 = 𝑝

  1 𝐶

• 𝑥 = 𝑝 − 𝑝2

  𝑦 = 𝑝

  3 𝐶

• 𝑥 = 𝑝 + 𝑝2

  𝑦 = 𝑝

  1 𝐶

• 𝑥 = 𝑝 + 𝑝2

  𝑦 = 𝑝

𝑦′ − 2𝑦 = 𝑒−𝑥 chiziqli differensial tenglamani yeching. Решите линейное дифференциальное уравнение 𝑦′ − 2𝑦 = 𝑒−𝑥. Solve a linear differential equation

𝑦′ − 2𝑦 = 𝑒−𝑥.

• 𝑦 = −𝑒𝑥 + 𝐶𝑒2𝑥

• 𝑦 =

  1 𝑥 + 𝑒

  2

  2𝑥𝐶

• 𝑦 = −𝑥 + 𝐶

• 𝑦 = 2𝑥 + 𝑒2𝑥𝐶

150. 𝑦′ + 2𝑦 = 𝑒−𝑥 chiziqli differensial tenglamani yeching. Решите линейное дифференциальное уравнение 𝑦′ + 2𝑦 = 𝑒−𝑥. Solve a linear differential equation

𝑦′ + 2𝑦 = 𝑒−𝑥

• 𝑦 = 𝑒−𝑥 + 𝐶𝑒−2𝑥

• 𝑦 =

  1 𝑥 + 𝑙𝑛𝑥 · 𝐶

  2

• 𝑦 = −𝑥 + 𝐶

• 𝑦 = 2𝑥 + 𝑒−2𝑥𝐶

𝑥2𝑦′ = 𝑥𝑦 + 𝑥2 bir jinsli tenglamani yeching. Решите однородное уравнение

𝑥2𝑦′ = 𝑥𝑦 + 𝑥2. Solve homogeneous equation 𝑥2𝑦′ = 𝑥𝑦 + 𝑥2.

• 𝑦 = 𝑥 · 𝑙𝑛𝑥 · 𝐶

• 𝑦 =

  1 𝑥 · 𝑙𝑛𝑥 · 𝐶

  2

• 𝑦 = −𝑥 · 𝑙𝑛𝑥 · 𝐶

• 𝑦 = 2𝑥 · 𝑙𝑛𝑥 · 𝐶

𝑥2𝑦′ = 𝑥𝑦 − 𝑥2 bir jinsli tenglamani yeching. Решите однородное уравнение

𝑥2𝑦′ = 𝑥𝑦 − 𝑥2. Solve homogeneous equation 𝑥2𝑦′ = 𝑥𝑦 − 𝑥2.

• 𝑦 = 𝑥 · 𝑙𝑛 𝐶

  𝑥

• 𝑦 = −𝑥 · 𝑙𝑛 𝐶

  𝑥

• 𝑦 = 2𝑥 · 𝑙𝑛 𝐶

  𝑥

• 𝑦 =

  1 𝑥 · 𝑙𝑛 𝐶

  2 𝑥

𝑥𝑦′ = 𝑥 + 𝑦 bir jinsli tenglamani yeching. Решите однородное уравнение

𝑥𝑦′ = 𝑥 + 𝑦. Solove homogeneous equation 𝑥𝑦′ = 𝑥 + 𝑦.

• 𝑦 = 𝑥 · 𝑙𝑛𝑥 · 𝐶

• 𝑦 =

  1 𝑥 · 𝑙𝑛𝑥 · 𝐶

  2

• 𝑦 = −𝑥 · 𝑙𝑛𝑥 · 𝐶

• 𝑦 = 2𝑥 · 𝑙𝑛𝑥 · 𝐶

144. 𝑥𝑦′ − 2𝑦 = 0, 𝑦(2) = 1 Koshi masalasini yeching. Решите задачу Коши

𝑥𝑦′ − 2𝑦 = 0, 𝑦(2) = 1. Solve a Cauchy problem 𝑥𝑦′ − 2𝑦 = 0, 𝑦(2) = 1.

• 𝑦 = 𝑒2𝑥−4

• 𝑦 = 𝑒𝑥−4

• 𝑦 = 𝑒2𝑥

• 𝑦 = 𝑒2𝑥+4

𝑦′ = 𝑦

𝑥−1

, 𝑦(2) = 6 Koshi masalasini yeching. Решите задачу Коши 𝑦′ =

𝑦

𝑥−1

, 𝑦(2) = 6. Solve a Cauchy problem 𝑦′ = 𝑦

𝑥−1

, 𝑦(2) = 6.

• 𝑦 = 6𝑥 − 6

• 𝑦 = 𝑥 + 6

• 𝑦 = 6

• 𝑦 = 6𝑥

𝑦′ = 𝑦

𝑥+1

, 𝑦(2) = 6 Koshi masalasini yeching. Решите задачу Коши 𝑦′ =

𝑦

𝑥+1

, 𝑦(2) = 6. Solve a Cauchy problem 𝑦′ = 𝑦

𝑥+1

, 𝑦(2) = 6

• 𝑦 = 2𝑥 + 2

• 𝑦 = 2𝑥 + 1

• 𝑦 = 2𝑥

• 𝑦 = 𝑥 + 2