求微分方程 [tex=4.429x2.429]s4QumE5pv31BDaGg1MTOdCPqUnURPdvWlM30AVNdHlc=[/tex] 的通解.

求下列各微分方程的通解或满足初始条件的特解.[tex=4.429x2.429]eE9dXkpN2effVrNkAbXJmH3Y+bHoeYrnJT1/80kz96Ri9r4oHu41Zb18SNLXDhDM[/tex].

考察下列数列[tex=2.0x1.357]CjCvAldACdhCbOUJYZLY+0nRBLhCQFA+2tCS8je5CxI=[/tex]的变化趋势，判断是否有极限？若有极限，写出其极限值.[tex=4.429x2.429]7O41fxgR8khutExzgzJM+3AuYHQ/0hs8MLQ0SnJCIb0=[/tex].

下列积分中可直接用牛顿一莱布尼兹公式计算的是 未知类型：{'options': ['[tex=4.429x2.429]LeHfTm1EDLvENiRHF5LVd5/eXQ42o3OoxxpUYtPjavHgbU3Xg2rRK3fZa/32o4Rj[/tex]', '[tex=5.429x2.429]8b+hjoT15F7oDJ67WbRStTO7uzGOMOGea0G4kUhyCoZyA44zmw51ru5VzirNKeMn4kxepdUXuqn+J5H88cM+iA==[/tex]', '[tex=3.929x2.5]Du1DyH3mwdVzTlG55xliFQ6syY5aD84SlZkF2WA+nTFAgDHrmxZ5351AH9H2Vqa2k1/8Td1SlIWtAUFogA8mL3hNzOdKMI7B735LG3GoKBk=[/tex]', '[tex=3.857x2.429]uYo4SrtjkqYath3mU9F8mP1MXfz7c5QDEAXgTY06naHBkiDRyed8hXX7eLa3iCxN[/tex]'], 'type': 102}

下列积分中可直接用牛顿一莱布尼兹公式计算的是 未知类型：{'options': ['[tex=4.429x2.429]LeHfTm1EDLvENiRHF5LVd5/eXQ42o3OoxxpUYtPjavHgbU3Xg2rRK3fZa/32o4Rj[/tex]', '[tex=5.429x2.429]8b+hjoT15F7oDJ67WbRStTO7uzGOMOGea0G4kUhyCoZyA44zmw51ru5VzirNKeMn4kxepdUXuqn+J5H88cM+iA==[/tex]', '[tex=3.929x2.5]Du1DyH3mwdVzTlG55xliFQ6syY5aD84SlZkF2WA+nTFAgDHrmxZ5351AH9H2Vqa2k1/8Td1SlIWtAUFogA8mL3hNzOdKMI7B735LG3GoKBk=[/tex]', '[tex=3.857x2.429]uYo4SrtjkqYath3mU9F8mP1MXfz7c5QDEAXgTY06naHBkiDRyed8hXX7eLa3iCxN[/tex]'], 'type': 102}

下列积分中可直接用牛顿一莱布尼兹公式计算的是 未知类型：{'options': ['[tex=4.429x2.429]LeHfTm1EDLvENiRHF5LVd5/eXQ42o3OoxxpUYtPjavHgbU3Xg2rRK3fZa/32o4Rj[/tex]', '[tex=5.429x2.429]8b+hjoT15F7oDJ67WbRStTO7uzGOMOGea0G4kUhyCoZyA44zmw51ru5VzirNKeMn4kxepdUXuqn+J5H88cM+iA==[/tex]', '[tex=3.929x2.5]Du1DyH3mwdVzTlG55xliFQ6syY5aD84SlZkF2WA+nTFAgDHrmxZ5351AH9H2Vqa2k1/8Td1SlIWtAUFogA8mL3hNzOdKMI7B735LG3GoKBk=[/tex]', '[tex=3.857x2.429]uYo4SrtjkqYath3mU9F8mP1MXfz7c5QDEAXgTY06naHBkiDRyed8hXX7eLa3iCxN[/tex]'], 'type': 102}

下列积分中可直接用牛顿一莱布尼兹公式计算的是 未知类型：{'options': ['[tex=4.429x2.429]LeHfTm1EDLvENiRHF5LVd5/eXQ42o3OoxxpUYtPjavHgbU3Xg2rRK3fZa/32o4Rj[/tex]', '[tex=5.429x2.429]8b+hjoT15F7oDJ67WbRStTO7uzGOMOGea0G4kUhyCoZyA44zmw51ru5VzirNKeMn4kxepdUXuqn+J5H88cM+iA==[/tex]', '[tex=3.929x2.5]Du1DyH3mwdVzTlG55xliFQ6syY5aD84SlZkF2WA+nTFAgDHrmxZ5351AH9H2Vqa2k1/8Td1SlIWtAUFogA8mL3hNzOdKMI7B735LG3GoKBk=[/tex]', '[tex=3.857x2.429]uYo4SrtjkqYath3mU9F8mP1MXfz7c5QDEAXgTY06naHBkiDRyed8hXX7eLa3iCxN[/tex]'], 'type': 102}

下列积分中可直接用牛顿一莱布尼兹公式计算的是 未知类型：{'options': ['[tex=4.429x2.429]LeHfTm1EDLvENiRHF5LVd5/eXQ42o3OoxxpUYtPjavHgbU3Xg2rRK3fZa/32o4Rj[/tex]', '[tex=5.429x2.429]8b+hjoT15F7oDJ67WbRStTO7uzGOMOGea0G4kUhyCoZyA44zmw51ru5VzirNKeMn4kxepdUXuqn+J5H88cM+iA==[/tex]', '[tex=3.929x2.5]Du1DyH3mwdVzTlG55xliFQ6syY5aD84SlZkF2WA+nTFAgDHrmxZ5351AH9H2Vqa2k1/8Td1SlIWtAUFogA8mL3hNzOdKMI7B735LG3GoKBk=[/tex]', '[tex=3.857x2.429]uYo4SrtjkqYath3mU9F8mP1MXfz7c5QDEAXgTY06naHBkiDRyed8hXX7eLa3iCxN[/tex]'], 'type': 102}

下列积分中可直接用牛顿一莱布尼兹公式计算的是 未知类型：{'options': ['[tex=4.429x2.429]LeHfTm1EDLvENiRHF5LVd5/eXQ42o3OoxxpUYtPjavHgbU3Xg2rRK3fZa/32o4Rj[/tex]', '[tex=5.429x2.429]8b+hjoT15F7oDJ67WbRStTO7uzGOMOGea0G4kUhyCoZyA44zmw51ru5VzirNKeMn4kxepdUXuqn+J5H88cM+iA==[/tex]', '[tex=3.929x2.5]Du1DyH3mwdVzTlG55xliFQ6syY5aD84SlZkF2WA+nTFAgDHrmxZ5351AH9H2Vqa2k1/8Td1SlIWtAUFogA8mL3hNzOdKMI7B735LG3GoKBk=[/tex]', '[tex=3.857x2.429]uYo4SrtjkqYath3mU9F8mP1MXfz7c5QDEAXgTY06naHBkiDRyed8hXX7eLa3iCxN[/tex]'], 'type': 102}

下列积分中可直接用牛顿一莱布尼兹公式计算的是 未知类型：{'options': ['[tex=4.429x2.429]LeHfTm1EDLvENiRHF5LVd5/eXQ42o3OoxxpUYtPjavHgbU3Xg2rRK3fZa/32o4Rj[/tex]', '[tex=5.429x2.429]8b+hjoT15F7oDJ67WbRStTO7uzGOMOGea0G4kUhyCoZyA44zmw51ru5VzirNKeMn4kxepdUXuqn+J5H88cM+iA==[/tex]', '[tex=3.929x2.5]Du1DyH3mwdVzTlG55xliFQ6syY5aD84SlZkF2WA+nTFAgDHrmxZ5351AH9H2Vqa2k1/8Td1SlIWtAUFogA8mL3hNzOdKMI7B735LG3GoKBk=[/tex]', '[tex=3.857x2.429]uYo4SrtjkqYath3mU9F8mP1MXfz7c5QDEAXgTY06naHBkiDRyed8hXX7eLa3iCxN[/tex]'], 'type': 102}