求解方程: [tex=6.429x1.571]PIzhbkt264aM659AcX7mQYdoiGDbPjFNZBlgkLcNV/zO6uLNtBGGwNiBOWeYVL+H[/tex]
解:特解 [tex=4.0x2.357]IHLwOryojnkN+XPCylnnlty+gdZ3r4nTGTnjGH8lmUI=[/tex] 取变换 [tex=4.5x2.357]unCxnbYZKIyOU9PKhL7i+RMC2mGByEPeRxwhbZWJQQs=[/tex]方程化为 [tex=6.214x1.357]uj/kenWUblOovEGJpu9xuZX7vU5+rXpCh6g6JkkiskIRXjl40vmwHdjfkaOQJXUO[/tex] 令 [tex=3.071x1.429]zxGQLSgmzJ+SjX5SbHXmDg==[/tex] 得 [tex=5.214x1.429]zaz5vJXRYwikg+07JBjMNoVowGVhGze30tCmr0jM0H4=[/tex] 有解 [tex=14.571x2.643]WZDATW9ZTBbjCWDLADGfuXjGObkZw8c7bsvBy2hH6HqpqAO/WxZDQRS4CmFXCDe0mLI4mupJtEUPqnTpEzuYBQ==[/tex] 方程的通解为 [tex=10.857x2.786]CBrqAJEZRts6APeefaS8xwyCPTnWuSeZT+7SA5lRBjN+brEbwcAjvv1OsXoOBUvE[/tex] [tex=8.0x2.643]20YBGgYyOgdY+tkw86ksTeY4wQ6JjznM1YBZKI6Xp7o=[/tex]或利用通解式 [tex=24.071x2.786]8ChrzW+Vbup7Ar3gXChjpgjlWbNIvvOlgTZgE+krBuJjdKOftbdY6XKQk50lHFF+YfJV6/ITSV6olyn+iQwlqQIw6DhfTAl+YFkFdL5QDS2aFCo8RMu6cEiJfWvZWYcd2Sj9pZrunRJs2V+7/OTJbfn9A4aCoZBiNSdFXesvG2ecTyBiYHxWzQt1Do77KRUfHyXcay+E/4gpZ751rzSELhMcsBZYQIdixb1EK0g1KGM=[/tex],得 [tex=27.5x2.786]CBrqAJEZRts6APeefaS8x00RTq6d2Kpq8uRUA0Uc761uCpWxTUywXDHfONVMgHn1iLHKSr5IwKkDdImQ5G02zK1Hlaifg1Mp9cBJhbhRv5LW1LokmpXof7HMoNg2M7b6SVyGcSr3wrsHgyon5ugSYfjcQC9UCDNMSGB+7abIl/3SgbvViAnFhiwFTM9isOAR8DZ09oYM3zyeUKbA+nAcJAcO12NvBFS8DTYB6btq++A=[/tex]
举一反三
- 用幂级数解法求解方程 [tex=6.071x1.429]7/NebOJ+accrjPN+Co+D9eABCZdXJA+HGPdiTwzfWgQ=[/tex]
- 证明方程 [tex=5.643x2.643]veMIbIHrCKyfJD6p8CsZieV/mC7jauoF+RoXvFL11rxcZNCHFWI1bp9PcV7QjXfuLz8jFJG3FjoRv6p+Zfkmnw==[/tex] 经变换 $x y=u$ 可化为变量分离方程,并由此求解方程:[tex=8.429x1.571]8HRcqzX3v4Y2lj/bxKtUWyTaeJGkmxPo/lnb2KrFyUkh3bTJjq7hgObaU0hI8NF68rCBoV64ntgfXyGigpHhLQ==[/tex]
- 求解方程:[tex=9.857x1.429]gRMBs004m5aa5Vvioef+gLIbRxGw7MWxWe0KgNx6hpC09y/LBV2Mm46diB9CHPE5fh0mC3gI653D9HzVbW+T6koLpBGQH6Gf5MlIVFZMWJ0=[/tex]
- 求解下列方程:[tex=7.714x1.5]/Cg8FBIIS08CVW3wDUZul+Zs3IpmgOjF0QYEGC8KVtLXLwAEwAOzxyCwVyLhcLLp[/tex]
- 求解方程: [tex=7.357x1.429]C1cW9lHEhpjBlL80QKmte5eQ+mtahC5BYO+uJhNxP7jolhp/GAbStY6cPwgMtTqJ[/tex]
内容
- 0
求解下列方程:[tex=8.5x1.571]Fg2aE5vQmi7rtUwGmYvqQxs9vrxhqbsfE5oG4bdm+Qa23qdyIFlozX21L2Eo24Es[/tex]
- 1
求解方程:[tex=9.857x1.429]gRMBs004m5aa5Vvioef+gLIbRxGw7MWxWe0KgNx6hpC09y/LBV2Mm46diB9CHPE5fh0mC3gI653D9HzVbW+T6koLpBGQH6Gf5MlIVFZMWJ0=[/tex]
- 2
求解方程 [tex=9.643x1.429]KY8UeqjqRwfPCHaOAlTSEwmyb7+gsNJEj6vfNwG7phXorcRCRRnciBMOZ54TLFM88a3jue/DY6fg1dDhdGMRIp1RZIw1rQ+JhjNwbWDF2GI=[/tex].
- 3
求解方程:[tex=12.286x1.5]o2HeQ9QIjldMMVZlonu8gHZ8EQ12sQ3XbQj5481otaARh5dLEZK/6NcFO12HrnoH[/tex]
- 4
求解方程:[tex=13.143x1.429]3d0Pby/YoevVICHDAyxlTn9mjJV+2qrwxBqZjPIBBJqB6XiRCcf96tmEFqtYdNz9UfAdRpBDjLaZuynctVG6AA==[/tex]